Kurihara, Masato

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics (Yagami)

Position

Professor

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Career 【 Display / hide 】

  • 1988.10
    -
    1992.09

    東京都立大学理学部助手

  • 1991.09
    -
    1993.08

    Harvard University, Department of Mathematics, Visiting scholar

  • 1992.10
    -
    2005.03

    東京都立大学大学院理学研究科助教授

  • 2005.04
    -
    Present

    慶應義塾大学理工学部数理科学科教授

  • 2008.04
    -
    2012.03

    大阪大学大学院理学研究科招聘教授

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Academic Background 【 Display / hide 】

  • 1984.03

    The University of Tokyo, Faculty of Science, Department of Mathematics

    University, Graduated

  • 1986.03

    The University of Tokyo, Graduate School, Division of Science, Mathematics

    Graduate School, Completed, Master's course

  • 1988.09

    The University of Tokyo, Graduate School, Division of Science, Mathematics

    Graduate School, Withdrawal before completion, Doctoral course

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Academic Degrees 【 Display / hide 】

  • Ph.D, The University of Tokyo, Dissertation, 1991.10

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Research Areas 【 Display / hide 】

  • Natural Science / Algebra

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Research Keywords 【 Display / hide 】

  • Number Theory

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Research Themes 【 Display / hide 】

  • Number Theory, 

    1984
    -
    Present

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Books 【 Display / hide 】

  • ガウスの数論世界をゆく--正多角形の作図から相互法則・数論幾何へ

    KURIHARA MASATO, 数学書房, 2017.05

  • Number Theory II Iwasawa theory and modular forms

    KUROKAWA NOBUSHIGE, KURIHARA MASATO, SAITO TAKESHI, Iwanami Publisher, 2005.02

  • Invitation to higher local fields

    KURIHARA MASATO and IVAN FESENKO, Coventry, England, 2000.12

  • Kenkichi Iwasawa Collected papers Vol. I, II

    I. Satake, G. Fujisaki, K. Kato, M. Kurihara, S. Nakajima 編, 2001

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Papers 【 Display / hide 】

  • On derivatives of Kato’s Euler system for elliptic curves

    Burns D., Kurihara M., Sano T.

    Journal of the Mathematical Society of Japan 76 ( 3 ) 855 - 919 2024.07

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  00255645

    　View Summary

    In this paper, we formulate a new conjecture concerning Kato’s Euler system for elliptic curves E over Q. This ‘Generalized Perrin-Riou Conjecture’ predicts a precise congruence relation between a Darmon-type derivative of the zeta element of E over an arbitrary real abelian field and the critical value of an appropriate higher derivative of the L-function of E over Q. We prove the conjecture specializes in the relevant case of analytic rank one to recover Perrin-Riou’s conjecture on the logarithms of zeta elements, and also that, under mild technical hypotheses, the ‘order of vanishing’ part of the conjecture is unconditionally valid in arbitrary rank. This approach also allows us to prove a natural higher-rank generalization of Rubin’s formula concerning derivatives of p-adic L-functions and to establish an explicit connection between the p-part of the classical Birch and Swinnerton-Dyer formula and the Iwasawa main conjecture in arbitrary rank and for arbitrary reduction at p. In a companion article we prove that the approach developed here also provides a new interpretation of the Mazur–Tate conjecture that leads to the first (unconditional) theoretical evidence in support of this conjecture for curves of strictly positive rank.

  • Minimal resolutions of Iwasawa modules

    Takenori Kataoka, Masato Kurihara

    Research in Number Theory 10 ( 3 ) 1 - 23 2024.06

    Research paper (scientific journal), Joint Work, Accepted

    　View Summary

    In this paper, we study the module-theoretic structure of classical Iwasawa modules. More precisely, for a finite abelian p-extension K/k of totally real fields and the cyclotomic Zp-extension K∞/K, we consider XK∞,S=Gal(MK∞,S/K∞) where S is a finite set of places of k containing all ramifying places in K∞ and archimedean places, and MK∞,S is the maximal abelian pro-p-extension of K∞ unramified outside S. We give lower and upper bounds of the minimal numbers of generators and of relations of XK∞,S as a Zp[[Gal(K∞/k)]]-module, using the p-rank of Gal(K/k). This result explains the complexity of XK∞,S as a Zp[[Gal(K∞/k)]]-module when the p-rank of Gal(K/k) is large. Moreover, we prove an analogous theorem in the setting that K/k is non-abelian. We also study the Iwasawa adjoint of XK∞,S, and the minus part of the unramified Iwasawa module for a CM-extension. In order to prove these theorems, we systematically study the minimal resolutions of XK∞,S.

  • Some analytic quantities yielding arithmetic information about elliptic curves

    Masato Kurihara

    A publication of Tata Institute of Fundamental Research, Arithmetic Geometry    345 - 384 2024

    Research paper (international conference proceedings), Single Work, Accepted

    　View Summary

    For a rational elliptic curve E and a positive integer n, satisfying some properties, we introduce analytic quantities delta_{n} using modular symbols, and give conjectures that these quantities control the maps of reduction modulo primes dividing n on E(Q). These conjectures also describe the structure of Selmer groups and the Tate-Shafarevich group of E. One of the aims of this paper is to provide an exposition on the theory of these analytic quantities. In the direction of the conjectures, we generalize, to all good reduction primes p, an injectivity theorem which was proven only for good ordinary primes in our earlier paper.

  • Fitting ideals of p-ramified Iwasawa modules over totally real fields

    Cornelius Greither, Takenori Kataoka, Masato Kurihara

    Selecta Mathematica (Selecta Mathematica, New Series)  28 ( 1 ) 1 - 48 2022.02

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  10221824

    　View Summary

    We completely calculate the Fitting ideal of the classical p-ramified Iwasawa module for any abelian extension K/k of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results where we had to assume that only p-adic places may ramify in K/k. One of the important ingredients is the computation of some complexes in appropriate derived categories.

  • Notes on the dual of the ideal class groups of CM-fields

    Masato Kurihara

    Journal de Théorie des Nombres de Bordeaux (Journal de Theorie des Nombres de Bordeaux)  33 ( 3.2 ) 971 - 996 2021

    Research paper (scientific journal), Single Work, Accepted,  ISSN  12467405

    　View Summary

    In this paper, for a CM abelian extension K/k of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the T-ray class group of K for a set T of primes as a Gal(K/k)-module. Here, we emphasize that we consider the full class group, and do not throw away the ramifying primes (the object we study is not the quotient of the class group by the subgroup generated by the classes of ramifying primes). We prove that our conjecture is a consequence of the equivariant Tamagawa number conjecture, and also prove the Iwasawa theoretic version of our conjecture.

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Reviews, Commentaries, etc. 【 Display / hide 】

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Presentations 【 Display / hide 】

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 岩澤理論とオイラー系理論の新展開

    2022.04
    -
    2026.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 基盤研究(B), Principal investigator

  • New Development of Iwasawa theory

    2019.04
    -
    2023.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Principal investigator

  • 数論と幾何学を核とする数理科学国際連携研究拠点形成

    2014.04
    -
    2019.03

    Masato Kurihara, Principal investigator

  • 科学研究費補助金基盤研究(A)　岩澤理論の発展と展開

    2013.04
    -
    2018.03

    Grant-in-Aid for Scientific Research, Principal investigator

  • 岩澤理論の発展と展開

    2013.04
    -
    2018.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A) , Principal investigator

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Works 【 Display / hide 】

  • ガウスの数論から現代数学へ I, II, III, IV, V

    栗原将人

    2022.02
    -
    2022.08
    , 

    Single

  • 現象を通じて見る岩澤理論

    数学セミナー, 

    2018.01
    , 

    Other

  • ガウスと相互法則 I, II

    数学セミナー, 

    2017.07
    -
    2017.08
    , 

    Other

  • J.-P.セールの本をめぐってーブルバキ随想

    KURIHARA MASATO

    2001.12
    , 

    Other, Single

  • バーチ、スウィナートンダイヤー予想

    KURIHARA MASATO

    2000.11
    , 

    Other, Single

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Awards 【 Display / hide 】

  • Mathematical Society of Japan, Algebra Prize

    KURIHARA MASATO, 2002.03, 日本数学会代数学分科会, Studies on Iwasawa theory

    Type of Award： Award from Japanese society, conference, symposium, etc.

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Courses Taught 【 Display / hide 】

  • TOPICS IN INTEGRATED MATHEMATICAL SCIENCES 2

    2024

  • MATHEMATICS 2B

    2024

  • MATHEMATICS 2A

    2024

  • LINEAR ALGEBRA

    2024

  • LIBERAL ARTS AND SCIENCES SEMINAR 2

    2024

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Social Activities 【 Display / hide 】

  • Chief editor of Tokyo Journal of Mathematics

    2013.04
    -
    2020.03

  • editor of Tokyo Journal of Mathematics

    2006.04
    -
    2020.03

  • editor of International Journal of Number Theory

    2004
    -
    2008
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Memberships in Academic Societies 【 Display / hide 】

  • American Mathematical Society, 

    2019.01
    -
    Present

  • 日本数学会評議員, 

    2007.03
    -
    2009.03

  • 日本数学会代数学分科会運営委員, 

    2003.09
    -
    Present

  • 雑誌「数学」編集委員, 

    1998.07
    -
    2000.06

  • 日本数学会, 

    1987
    -
    Present
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Committee Experiences 【 Display / hide 】

  • 2013.04
    -
    2020.03

    編集委員長, Tokyo Journal of Mathematics

  • 2007.03
    -
    2009.03

    Board of Councillors, 日本数学会

  • 2006.04
    -
    2020.03

    Editor, Tokyo Journal of Mathematics

  • 2004
    -
    2008

    editor, International Journal of Number Theory

  • 2003.09
    -
    Present

    運営委員, 日本数学会代数学分科会

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