Kurihara, Masato

写真a

Affiliation

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

Position

Professor

Related Websites

External Links
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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 】

  • 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.

  • On Stark elements of arbitrary weight and their p-adic families

    David Burns, Masato Kurihara and Takamichi Sano

    Development of Iwasawa Theory — the Centennial of K. Iwasawa's Birth, Advanced Studies in Pure Mathematics 86   113 - 140 2020.12

    Research paper (scientific journal), Joint Work, Accepted

  • The second syzygy of the trivial G-module, and an equivariant main conjecture

    Cornelius Greither, Masato Kurihara and Hibiki Tokio

    Development of Iwasawa Theory — the Centennial of K. Iwasawa's Birth, Advanced Studies in Pure Mathematics 86   317 - 349 2020.12

    Research paper (scientific journal), Joint Work, Accepted

  • On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction

    Chan-Ho Kim and Masato Kurihara

    International Mathematics Research Notices （International Mathematics Research Notices)  2021 （ 14 ） 10559 - 10599 2021.07

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  10737928

    　View Summary

    In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of an elliptic curve over $\mathbb{Q}$. Especially, we present a proof of the "weak main conjecture"à la Mazur and Tate for elliptic curves with good (supersingular) reduction at an odd prime $p$. We also prove the "strong main conjecture"suggested by the second named author under the validity of the $\pm $-main conjecture and the vanishing of a certain error term. The key idea is the explicit comparison among "finite layer objects", "$\pm $-objects", and "fine objects"in Iwasawa theory. The case of good ordinary reduction is also treated.

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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 】

  • Euler and Kolyvagin systems of Gauss sum type

    Masato Kurihara

    Arithmetic of L-functions (Instituto de Ciencias Matematicas (Madrid)) , 

    2023.05
    , 

    Oral presentation (invited, special)

  • いくつかの Selmer module の導入とその性質

    栗原将人

    Dasgupta Kakde の最近の仕事とその周辺 workshop (慶應義塾大学理工学部) , 

    2022.02

  • Dasgupta Kakde の最近の仕事とその周辺 Overview

    栗原将人

    Dasgupta Kakde の最近の仕事とその周辺 (慶應義塾大学理工学部) , 

    2022.02

  • Some analytic quantities in the arithmetic of elliptic curves

    Masato Kurihara

    The 9th East Asia Number Theory Conference, 

    2021.08
    , 

    Oral presentation (general)

  • Survey on the Brumer-Stark conjecture and the proof by Dasgupta and Kakde

    栗原将人

    代数的整数論とその周辺, 

    2020.12
    , 

    Oral presentation (general)

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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 1

    2023

  • TOPICS IN ALGEBRA B

    2023

  • MATHEMATICS 4B

    2023

  • MATHEMATICS 4A

    2023

  • LINEAR ALGEBRA

    2023

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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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