TOHOKU UNIVERSITY Researchers

Details of the Researcher

Home

日本語 English

Takuya Yamauchi

Section

Graduate School of Science

Job title

Associate Professor

Degree

博士（理学）（広島大学）
修士（理学）（広島大学）

researchmap

https://researchmap.jp/7000019122

J-GLOBAL ID

201701004409612918

e-Rad No.

90432707

Education 4

Hiroshima University

- 2002
Hiroshima University　Graduate school of science　Mathematics

- 2002
Hiroshima University　Faculty of Science

- 2000
Hiroshima University　School of Science　Mathematics

- 2000

Committee Memberships 2

日本数学会　会員
Mathematical Society of Japan　Member

Professional Memberships 2

Mathematical Society of Japan
日本数学会

Research Interests 7

Galois representations, Serre conjecture
楕円曲線
Modular curves
elliptic curves
Automarphic forms
モジュラー曲線
保型形式

Research Areas 1

Natural sciences / Algebra /

Awards 1

JMSJ論文賞

2024　日本数学会　Harder’s conjecture I

Papers 44

Restriction of modular forms on E_{7,3} to Sp_6

Henry H. Kim, Takuya Yamauchi

Research in Number Theory　11　(3)　2025/07/10
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s40993-025-00649-3 　

ISSN： 2522-0160

eISSN： 2363-9555
An inductive formula for the Gross-Keating invariant of a quadratic form

Sungmun Cho, Tamotsu Ikeda, Hidenori Katsurada, Chul-hee Lee, Takuya Yamauchi

Tohoku Mathematical Journal　77　(1)　2025/03/01
Publisher: Mathematical Institute, Tohoku University
DOI： 10.2748/tmj.20230426 　

ISSN： 0040-8735
Transfers of some Hecke elements for possibly ramified base change in GLn

Takuya Yamauchi

Kyoto Journal of Mathematics　65　(1)　2025/02/01
Publisher: Duke University Press
DOI： 10.1215/21562261-2024-0012 　

ISSN： 2156-2261
An explicit formula for the extended Gross-Keating datum of a quadratic form

Sungmun Cho, Tamotsu Ikeda, Hidenori Katsurada, Chul-hee Lee, Takuya Yamauchi

Mathematics of Computation　2025/01/23
Publisher: American Mathematical Society (AMS)
DOI： 10.1090/mcom/4050 　

ISSN： 0025-5718

eISSN： 1088-6842

More details Close

<p>In this paper, we give a formula for the extended Gross-Keating datum of a half-integral symmetric matrix over a finite extension of (for ) or a finite unramified extension of . As an application, we describe an explicit formula for the Siegel series for . We also present the details of algorithms implemented in a Mathematica package to compute the extended Gross-Keating datum and the Siegel series.</p>
Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields

Alexandru Ghitza, Takuya Yamauchi

Journal de théorie des nombres de Bordeaux　36　(2)　637-660　2024/11/13
Publisher: Cellule MathDoc/Centre Mersenne
DOI： 10.5802/jtnb.1291 　

eISSN： 2118-8572
Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Algebra & Number Theory　18　(5)　993-1038　2024/04/16
Publisher: Mathematical Sciences Publishers
DOI： 10.2140/ant.2024.18.993 　

ISSN： 1937-0652

eISSN： 1944-7833
Distribution of Hecke eigenvalues for holomorphic Siegel modular forms

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Acta Arithmetica　215　(2)　161-177　2024
Publisher: Institute of Mathematics, Polish Academy of Sciences
DOI： 10.4064/aa230831-6-5 　

ISSN： 0065-1036

eISSN： 1730-6264
Isogeny graphs on superspecial abelian varieties: eigenvalues and connection to Bruhat–Tits buildings

Yusuke Aikawa, Ryokichi Tanaka, Takuya Yamauchi

Canadian Journal of Mathematics　76　(6)　1891-1916　2023/10/20
Publisher: Canadian Mathematical Society
DOI： 10.4153/s0008414x23000676 　

ISSN： 0008-414X

eISSN： 1496-4279

More details Close

Abstract We study for each fixed integer $g \ge 2$, for all primes $\ell $ and p with $\ell \neq p$, finite regular directed graphs associated with the set of equivalence classes of $\ell $-marked principally polarized superspecial abelian varieties of dimension g in characteristic p, and show that the adjacency matrices have real eigenvalues with spectral gaps independent of p. This implies a rapid mixing property of natural random walks on the family of isogeny graphs beyond the elliptic curve case and suggests a potential construction of the Charles–Goren–Lauter-type cryptographic hash functions for abelian varieties. We give explicit lower bounds for the gaps in terms of the Kazhdan constant for the symplectic group when $g \ge 2$. As a byproduct, we also show that the finite regular directed graphs constructed by Jordan and Zaytman also has the same property.
Higher level cusp forms on exceptional group of type E7

Henry H. Kim, Takuya Yamauchi

Kyoto Journal of Mathematics　63　(3)　2023/08/01
Publisher: Duke University Press
DOI： 10.1215/21562261-10607364 　

ISSN： 2156-2261
Harder's conjecture I Peer-reviewed

Hiraku ATOBE, Masataka CHIDA, Tomoyoshi IBUKIYAMA, Hidenori KATSURADA, Takuya YAMAUCHI

Journal of the Mathematical Society of Japan　-1　(-1)　2023/03/14
Publisher: Mathematical Society of Japan (Project Euclid)
DOI： 10.2969/jmsj/87988798 　

ISSN： 0025-5645
The weight reduction of mod p Siegel modular forms for $$GSp_4$$ and theta operators

Takuya Yamauchi

Mathematische Zeitschrift　303　(1)　2022/12/07
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00209-022-03153-x 　

ISSN： 0025-5874

eISSN： 1432-1823
Period of the Ikeda type lift for the exceptional group of type E_{7,3}

Hidenori Katsurada, Henry H. Kim, Takuya Yamauchi

Mathematische Zeitschrift　302　(1)　559-588　2022/06/27
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00209-022-03057-w 　

ISSN： 0025-5874

eISSN： 1432-1823
Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences Peer-reviewed

Sungmun Cho, Shunsuke Yamana, Takuya Yamauchi

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg　92　(1)　27-52　2022/04/27
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s12188-022-00256-4 　

ISSN： 0025-5858

eISSN： 1865-8784
A remark on conductor, depth and principal congruence subgroups Peer-reviewed

Michitaka Miyauchi, Takuya Yamauchi

Journal of Algebra　592　424-434　2022/02
Publisher: Elsevier BV
DOI： 10.1016/j.jalgebra.2021.10.032 　

ISSN： 0021-8693
Congruences of Siegel Eisenstein series of degree two Peer-reviewed

Takuya Yamauchi

manuscripta mathematica　166　(3-4)　589-603　2020/11/11
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00229-020-01256-5 　

ISSN： 0025-2611

eISSN： 1432-1785
Equidistribution theorems for holomorphic Siegel modular forms for $$GSp_4$$; Hecke fields and n-level density

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Mathematische Zeitschrift　295　(3-4)　917-943　2020/08
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00209-019-02378-7 　

ISSN： 0025-5874

eISSN： 1432-1823
A reformulation of the Siegel series and intersection numbers Peer-reviewed

Sungmun Cho, Takuya Yamauchi

Mathematische Annalen　377　(3-4)　1757-1826　2020/05/15
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00208-020-01999-2 　

ISSN： 0025-5831

eISSN： 1432-1807
An equidistribution theorem for holomorphic siegel modular forms for GSP4 and its applications

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Journal of the Institute of Mathematics of Jussieu　19　(2)　351-419　2020/03/01
Publisher: Cambridge University Press
DOI： 10.1017/S147474801800004X 　

ISSN： 1475-3030 1474-7480
Non-vanishing of Miyawaki type lifts

Henry H. Kim, Takuya Yamauchi

Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg　89　(2)　117-134　2019/10/01
Publisher: Springer
DOI： 10.1007/s12188-019-00207-6 　

ISSN： 0025-5858
On Prym varieties for the coverings of some singular plane curves Peer-reviewed

Lubjana Beshaj, Takuya Yamauchi

manuscripta mathematica　158　(1-2)　205-222　2018/03/08
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00229-018-1018-z 　

ISSN： 0025-2611

eISSN： 1432-1785
On the class numbers of the fields of the p n -torsion points of elliptic curves over Q

Fumio Sairaiji, Takuya Yamauchi

Journal de Theorie des Nombres de Bordeaux　30　(3)　893-915　2018
Publisher: Institut de Mathematique de Bordeaux
DOI： 10.5802/jtnb.1056 　

ISSN： 2118-8572 1246-7405
A Miyawaki type lift for $$\textit{GSpin}(2,10)$$ GSpin ( 2 , 10 ) Peer-reviewed

Henry H. Kim, Takuya Yamauchi

Mathematische Zeitschrift　288　(1-2)　415-437　2017/05/09
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00209-017-1895-y 　

ISSN： 0025-5874

eISSN： 1432-1823
A uniform structure on subgroups of GL(n)(F-q) and its application to a conditional construction of Artin representations of GL(n) Peer-reviewed

Henry H. Kim, Takuya Yamauchi

JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY　32　(1)　75-99　2017/03

ISSN： 0970-1249

eISSN： 2320-3110
On some Siegel threefold related to the tangent cone of the Fermat quartic surface Peer-reviewed

Takeo Okazaki, Takuya Yamauchi

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS　21　(3)　585-630　2017

ISSN： 1095-0761

eISSN： 1095-0753
Cusp forms on the exceptional group of type E-7 Peer-reviewed

Henry H. Kim, Takuya Yamauchi

COMPOSITIO MATHEMATICA　152　(2)　223-254　2016/02

DOI： 10.1112/S0010437X15007538 　

ISSN： 0010-437X

eISSN： 1570-5846
On Intermediate Jacobians of Cubic Threefolds Admitting an Automorphism of Order Five Peer-reviewed

Bert van Geemen, Takuya Yamauchi

PURE AND APPLIED MATHEMATICS QUARTERLY　12　(1)　141-164　2016

ISSN： 1558-8599

eISSN： 1558-8602
A conditional construction of Artin representations for real analytic Siegel cusp forms of weight (2,1) Peer-reviewed

Henry H. Kim, Takuya Yamauchi

ADVANCES IN THE THEORY OF AUTOMORPHIC FORMS AND THEIR L-FUNCTIONS　664　225-260　2016

DOI： 10.1090/conm/664/13061 　

ISSN： 0271-4132
On the class numbers of the fields of the p(n)-torsion points of certain elliptic curves over Q Peer-reviewed

Fumio Sairaiji, Takuya Yamauchi

JOURNAL OF NUMBER THEORY　156　277-289　2015/11

DOI： 10.1016/j.jnt.2015.04.004 　

ISSN： 0022-314X

eISSN： 1096-1658
Bas Edixhoven and Jean-Marc Couveignes (eds.): Computational Aspects of Modular Forms and Galois Representations, Ann. of Math. Stud., 176, Princeton Univ. Press, 2011年，xii+425ページ．

山内卓也

数学　67　(3)　317-322　2015
Publisher: 一般社団法人日本数学会
DOI： 10.11429/sugaku.0673317 　

ISSN： 0039-470X
On the rational K-2 of a curve of GL(2) type over a global field of positive characteristic Peer-reviewed

Masataka Chida, Satoshi Kondo, Takuya Yamauchi

JOURNAL OF K-THEORY　14　(2)　313-342　2014/10

DOI： 10.1017/is014006024jkt272 　

ISSN： 1865-2433

eISSN： 1865-5394
An explicit computation of p-stabilized vectors Peer-reviewed

Michitaka MIYAUCHI, Takuya YAMAUCHI

Journal de Théorie des Nombres de Bordeaux　26　(2)　531-558　2014
Publisher: Cellule MathDoc/CEDRAM
DOI： 10.5802/jtnb.878 　

ISSN： 1246-7405

eISSN： 2118-8572
LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS Peer-reviewed

MICHITAKA MIYAUCHI, TAKUYA YAMAUCHI

International Journal of Number Theory　09　(08)　1995-2010　2013/12/02
Publisher: World Scientific Pub Co Pte Ltd
DOI： 10.1142/s179304211350070x 　

ISSN： 1793-0421

eISSN： 1793-7310

More details Close

Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GL_n(F). In this paper, we show that the Jacquet–Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations.
Endoscopic lifts to the Siegel modular threefold related to Klein’s cubic threefold Peer-reviewed

Takeo Okazaki, Takuya Yamauchi

American Journal of Mathematics　135　(1)　183-205　2013/02
Publisher: Project MUSE
DOI： 10.1353/ajm.2013.0002 　

eISSN： 1080-6377

More details Close

<p lang="en">Let ${\cal{A } }^{lev}_{11}$ be the moduli space of $(1,11)$-polarized abelian surfaces with a canonical level structure. Let $\chi$ be a primitive character of order 5 with conductor 11. In this paper we construct five endoscopic lifts $\Pi_i$, $0\le i\le 4$ from two elliptic modular forms $f\otimes\chi^i$ of weight 2 and $g\otimes\chi^i$ of weight 4 with complex multiplication by ${\Bbb{Q } } (\sqrt{-11})$ such that ${\Pi_i}_\infty$ gives a non-holomorphic differential form on ${\cal{A } }^{lev}_{11}$ for each $i$, $0\le i\le 4$. Then their spinor $L$-functions are of form $L(s-1,f\otimes\chi^i)L(s,g\otimes\chi^i)$ such that $L(s,g\otimes\chi^i)$ does not appear in the $L$-function of ${\cal{A } }^{lev}_{11}$ for any $i$, $0\le i\le 4$. The existence of such lifts is motivated by the computation of the $L$-function of Klein's cubic threefold which is a birational smooth model of ${\cal{A } }^{lev}_{11}$.</p>
The Rank of Jacobian Varieties over the Maximal Abelian Extensions of Number Fields: Towards the Frey-Jarden Conjecture Peer-reviewed

Fumio Sairaiji, Takuya Yamauchi

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES　55　(4)　842-849　2012/12

DOI： 10.4153/CMB-2011-140-5 　

ISSN： 0008-4395
A generalization of Sen-Brinon's theory Peer-reviewed

Takuya Yamauchi

MANUSCRIPTA MATHEMATICA　133　(3-4)　327-346　2010/11

DOI： 10.1007/s00229-010-0372-2 　

ISSN： 0025-2611
Q -motives and modular forms Peer-reviewed

Takuya Yamauchi

Journal of Number Theory　128　(6)　1485-1505　2008/06
Publisher: Elsevier BV
DOI： 10.1016/j.jnt.2008.03.001 　

ISSN： 0022-314X
On curves with split Jacobians Peer-reviewed

Takuya Yamauchi

COMMUNICATIONS IN ALGEBRA　36　(4)　1419-1425　2008/04

DOI： 10.1080/00927870701866622 　

ISSN： 0092-7872
The j-invariants of bielliptic modular curves X0(N Peer-reviewed

23　(2)　123-141　2008/02
A Siegel modular threefold and Saito-Kurokawa type lift to S 3(Γ1,3(2)) Peer-reviewed

Takeo Okazaki, Takuya Yamauchi

Mathematische Annalen　341　(3)　589-601　2008/01/08
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00208-007-0204-1 　

ISSN： 0025-5831

eISSN： 1432-1807
On rational torsion points of central \mathbb{Q}-curves Peer-reviewed

Fumio Sairaiji, Takuya Yamauchi

Journal de Théorie des Nombres de Bordeaux　20　(2)　465-483　2008
Publisher: Cellule MathDoc/CEDRAM
DOI： 10.5802/jtnb.637 　

ISSN： 1246-7405
THE MODULARITY OF Q-CURVES OF DEGREE 43 Peer-reviewed

Takuya Yamauchi

HOUSTON JOURNAL OF MATHEMATICS　34　(4)　1025-1035　2008

ISSN： 0362-1588
An observation on the cyclicity of the group of the F-p-rational points of abelian surfaces Peer-reviewed

Takuya Yamauchi

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS　24　(3)　307-318　2007/10

ISSN： 0916-7005
On Q-simple factors of Jacobian varieties of modular curves. Peer-reviewed

53　(2)　149-160　2007/02
On Q-simple factors of Jacobian varieties of quotient modular curves. Peer-reviewed

19　(3)　167-180　2004/03

Show all ︎Show first 5

Misc. 1

IKEDA TYPE CONSTRUCTION OF CUSP FORMS (Modular forms and automorphic representations)

1973　162-178　2015/11
Publisher: 京都大学数理解析研究所
ISSN： 1880-2818

Research Projects 17

New developments of automorphy of Galois representations and Serre conjecture.

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2019/04/01 - 2024/03/31
Study of arithmetic gometry by p-adic methods

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

Institution: Tohoku University

2018/04/01 - 2023/03/31
A experimental study of arithmetic local systems with geometric origins and unsolved problems in arithmetic geometry

TSUZUKI Nobuo, Yamauchi Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2015/04/01 - 2019/03/31

More details Close

While there are lots of unsolved problems in arithmetic geometry, it is difficult to construct explicit examples because of abstraction. Using the arithmetic family of higher dimensional Calabi-Yau varieties, which has been constructed by the author, over the projective line of invertible 2, (1) we show an irreducible component of the degenerated fiber is a rigid Calabi-Yau variety over the field of rational numbers, and prove the modularity and the algebraicity of cohomology classes, and (2) study a 2-adic model and construct a K3 surface over a real quadratic field with everywhere good reduction. We also study p-adic properties of Frobenius actions arithmetically, and prove the constancy of Newton polygons of arbitrary F-isocrystals on Abelian varieties. This result has not been known so far.
The geometry of Shimura varieties over positive characteristic and the development of Galois representations

Yamauchi Takuya, Chida Masataka, Miyauchi Michitaka

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

2015/04/01 - 2019/03/31

More details Close

The study conducted during the project was analysis of Serre weight. The Serre weight is a concept necessary to formulate modularity problem of the residual Galois representation, and specifies the possibility of the weights of the corresponding automorphic forms. In this research, we introduce the theta operators as one of the tools to analyze the Serre weight, and when the algebraic group is GSp4, we succeeded in giving a concrete expression of the theta operators. We use the modular lifting theorems to prove the Serre weight theorem in a fairly general case for GSp4 over totally real fields, and further a list of the possible Serre weight of corresponding automorphic forms was described completely in terms of the local properties of a given mod p Galois representation.
New developments in number theoretic geometry, topology, and algorithm

Matsumoto Makoto, TAMAGAWA AKIO, Mochizuki Shinichi, Hoshi Yuichiro, Tsuzuki Nobuo, Terasoma Tomohide, Saito Shuji, Tsuji Takeshi, Shiho Atsushi, Morita Shigeyuki, Shimada Ichiro, Kimura Shun-ichi, Kamada Seiichi, Sakuma Makoto, Ishii Akira, Takahashi Nobuyoshi, Hiranouchi Toshiro, Haramoto Hiroshi, Kaneko Masanobu, Taguchi Yuichiro, Furusho Hidekazu, Nishimura Takuji, Hagita Mariko, Yamauchi Takuya, Asakura Masanori, Mizusawa Yasushi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

2011/04/01 - 2016/03/31

More details Close

We studied pure mathematics such as number theory, algebra, geometry, in an interdisciplinary manner. In addition, we studied there application in other branch of science and engineering. In pure mathematics side, we constructed a mixed elliptic motif obtained from universal family of elliptic curves. Also, given an l-adic linear representation of arithmetic fundamental group of an algebraic curve, we compared the image of the representation and the image of the Galois group of k-rational point of curves. As for applicational research, we developped a fast numerical integration algorithm based on quasi-Monte Carlo. The method depends on a point set (called Niederreiter-Xing point sets) whose basis is in the theory of rational points of algebraic curves). We introduced a new criteria for uniformity of point set named WAFOM, and our algorithm uses point sets obtained by scrambling Niederreiter-Xing point sets whose WAFOM value is small. Its effectiveness is empirically confirmed.
Automorphic forms, algebraic varieties and Iwasawa theory

OKAZAKI Takeo, YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

Institution: Nara Women's University

2012/04/01 - 2015/03/31

More details Close

We established functional equations for automorphic representations of GU(2,2), and a New form theory corresponding to them. We call D-paramodular subgroups which fix the new forms. In particular, when the automorphic representation is distinguished, it has a D-paramodular Shalika period. By considering the theta correspondence between GSp(4) and GU(2,2), we give a proof for a conjecture of van Geemen and van Straten.
Integral structures of arithmetic differential equations and geometries behind them

TSUZUKI Nobuo, YAMAUCHI Takuya, TAKAHASHI Nobuyoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2012/04/01 - 2015/03/31

More details Close

We studied properties of the arithemtic family of Calabi-Yau varieties, constructed by the representative of this research, for which the period integral is a generalized hypergeometric functions. In particular, if the dimension is odd, we found a semistable family around a degenerated fiber such that the number of irreducible components of the special fiber is two among which the one is rational and the other has an interesting natures with respect to arithmetic geometry. In particuler, we proved the modularity of the special fiber in dimension 3. In the case of dimension 2, we constructed a semistable family over an extension of Z which is ramified only at 2 and got a K3 surface over an algebraic number field such that it has a good reduction everywhere.
The study of Galois deformations and an inductive structure of their automorphy

YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

Institution: Kagoshima University

2011/04/28 - 2015/03/31

More details Close

In this research project, the researcher carried out the program to study a correspondence between Galois representations (in the algebraic side) and automorphic forms (in the analytic side). Usually we understand it via p-adic Galois representations and it's reduction which is often called mod p representation. Then we have to divide the modularity problem into the type of mod p representation in question and plug them into the full modularity problem. In this project He studied the property of modular mod p representation so that any such representation could be reduced to a manageable class of mod p representation.
A study of arithemetic geometry by p-aidc methods

TSUZUKI NOBUO, KATO Fumiharu, SHIHO Atsushi, YAMAZAKI Takao, NAKAJIMA Yukiyoshi, YAMAUCHI Takuya, KAWAMURA Hisa-aki, ABE Tomoyuki, SUWA Noriyuki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2010/04/01 - 2014/03/31

More details Close

We investigated the foundation of p-adic methods in arithmetic geometry, rigid analytic technique and cohomology theory arising from differential forms (i.e., p-adic cohomology), and applied them to study arithmetic varieties. We construct p-adic Clemens-Schmid exact sequence for semistable families over algebraic curves of positive characteristic, which is a p-adic analogue of exact sequence describing kernel and cokernel of monodromy operations for semistable families over the complex unit disk. We studied the purity theorem for isocrystals and established the full faithfulness of restriction functors to open subschemes for isocrystals on geometrically unibranch varieties of positive characteristic. As a consequence, we proved pure of weight 1 for first rigid cohomology of proper and geometrically unibranch varieties. We also developed the weight theory in p-adic cohomology and the theory of arithmetic D-modules.
A local and global study of arithmetic varieties determined by arithmetic differential equations

TSUZUKI Nobuo, YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2009 - 2011

More details Close

We constructed an arithmetic family of Calabi-Yau varieties on the projective line whose period integral is a generalized hypergeometric function, and determined the relative cohomology of Betti, de Rham, etale and crystalline realizations. This family is a higher dimensional version of Legenedre's family of elliptic curves. The family of Calabi-Yau is obtained by a desingularization which is given explicitly, and has a semistable degeneration at 0. The cohomologies can be calculated by applying weight spectral sequences. Moreover, we have a result on modularity for rational fibers.
Research on explicit constructions of motives associated to automorphic forms

YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

2007 - 2010

More details Close

(1) A construction of Siegel paramodular form corresponding to some rigid Calabi-Yau threefold. (2) A construction of endoscopic lifts associated to some Siegel modular variety and a computation of L-function of that variety. (3) A construction of a Calabi-Yau family having continuous Hodge number over the projective line minus three points and potential automorphy of each fiber. For (3), we explain more concretely. From local systems of rank one over the open curve U : projective line minus three points, by using convolution we construct hypergeometric sheaves F_n/U of rank n+1, weight n for each natural number n and then we construct a Calabi-Yau family whose middle cohomology sheave realizes F_n up to algebraic cycles when n is even. As an application, we prove potential automorphy of each fiber.
New developments in number theory and geometry : arithmetic topology, categorical arithmetic geometry, algorithm

MATSUMOTO Makoto, TAMAGAWA Akio, MOCHIZUKI Shinichi, TSUZUKI Nobuo, KIMURA Shunichi, TERASOMA Tomohide, MORITA Shigeyuki, HIROSE Susumu, MORITA Takehiko, YOSHINO Masafumi, NAGAI Yoshitaka, SUGAWA Toshiyuki, TAKAHASHI Nobuyoshi, KANEKO Masanobu, TAGUCHI Yuichirou, ITO Hiroyuki, NISHIMURA Takuji, SAITO Shuji, TSUJI Takeshi, MORITA Yoshiyuki, SHIMADA Ichirou, ISHII Akira, YAMAUCHI Takuya, SHIHO Atsushi, SAITO Mutsuo, HARAMOTO Hiroshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

Institution: Hiroshima University

2007 - 2010

More details Close

By using methods of geometric topology in arithmetic geometry, knowledges on topology (such as the cohomology of the mapping class groups) are utilized in researches on arithmetic geometry (such as outer Galois representations).(2)We developped a frame work to detect objects in arithmetic geometry by means of its combinatorial and categorical data.(3)We developped algebraic and geometric alogrithm for applications such as evaluation of pseudorandom number generators.
A study of arithmetic varieties by p-adic methods

TSUZUKI Nobuo, KATO Fumiharu, SHIHO Atsushi, NAKAJIMA Yoshiyuki, MATSUDA Shigeki, ITO Hiroyuki, KIMURA Shunichi, TAGUCHI Yuichiro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

2005 - 2008
代数曲線のヤコビ多様体の分解に関する研究 Competitive

2004 - 2006
A Research on the decomposition of Jacobian varieties Competitive

2002 - 2006
On decomposition of Jacobian Varieties Competitive

2002 - 2004
ヤコビ多様体の分解について Competitive

2002 - 2004

Show all Show first 5