Updated on 2024/11/15

写真a

 
SANO Takamichi
 
Organization
Graduate School of Science Department of Mathematics Associate Professor
School of Science Department of Mathematics
Title
Associate Professor
Affiliation
Institute of Science

Position

  • Graduate School of Science Department of Mathematics 

    Associate Professor  2022.04 - Now

  • School of Science Department of Mathematics 

    Associate Professor  2022.04 - Now

Degree

  • 博士(理学) ( Keio University )

Research Areas

  • Natural Science / Algebra

Professional Memberships

  • 日本数学会

      Domestic

Awards

  • 日本数学会賞建部賢弘奨励賞

    2017.09   同変玉河数予想とオイラー系、特にRubin-Stark元に関する研究

Job Career (off-campus)

  • 大阪大学   日本学術振興会特別研究員(PD)

    2016.04 - 2016.09

  • 慶應義塾大学   日本学術振興会特別研究員(PD)

    2015.04 - 2016.03

  • 慶應義塾大学   日本学術振興会特別研究員(DC1)

    2013.04 - 2015.03

Education

  • Keio University   Doctor's Course   Graduated/Completed

    2013.04 - 2015.03

  • Keio University   Master's Course   Graduated/Completed

    2011.04 - 2013.03

  • Keio University     Graduated/Completed

    2007.04 - 2011.03

Papers

  • On Euler systems for motives and Heegner points Reviewed

    Takenori Kataoka, Takamichi Sano

    Journal of the Association for Mathematical Research   2 ( 2 )   154 - 208   2024

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    Publishing type:Research paper (scientific journal)   International / domestic magazine:International journal  

    DOI: 10.56994/JAMR.002.002.001

  • On derivatives of Kato's Euler system for elliptic curves Reviewed International coauthorship

    David Burns, Masato Kurihara, Takamichi Sano

    Journal of the Mathematical Society of Japan   76 ( 3 )   855 - 919   2024( ISSN:00255645 ( eISSN:18811167

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    <p>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.</p>

    DOI: 10.2969/jmsj/90699069

  • On p-adic families of special elements for rank-one motives, Reviewed International coauthorship

    David Burns, Dominik Bullach, Takamichi Sano

    Transactions of the American Mathematical Society   376   5377 - 5407   2023.05

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    Publishing type:Research paper (scientific journal)   International / domestic magazine:International journal  

    DOI: https://doi.org/10.1090/tran/8929

  • On Euler systems for the multiplicative group over general number fields Reviewed International coauthorship

    David Burns, Alexandre Daoud, Takamichi Sano, Soogil Seo

    Publicacions Mathematiques   67 ( 1 )   89 - 126   2022.12

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    Publishing type:Research paper (scientific journal)   Kind of work:Joint Work   International / domestic magazine:International journal  

    DOI: 10.5565/PUBLMAT6712302

  • On higher special elements of p-adic representations Reviewed International coauthorship

    David Burns, Takamichi Sano, Kwok-Wing Tsoi

    International Mathematics Research Notices   2021 ( 20 )   15337 - 15411   2021.10

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    Publishing type:Research paper (scientific journal)   Kind of work:Joint Work  

  • On the theory of higher rank Euler, Kolyvagin and Stark systems Reviewed International coauthorship

    David Burns, Takamichi Sano

    International Mathematics Research Notices   2021 ( 13 )   10118 - 10206   2021.07

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    Publishing type:Research paper (scientific journal)   Kind of work:Joint Work  

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

    David Burns, Masato Kurihara, Takamichi Sano

    Advanced Studies in Pure Mathematics   86   113 - 140   2020

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    Publishing type:Research paper (international conference proceedings)   Kind of work:Joint Work  

  • On Iwasawa theory, zeta elements for G(m), and the equivariant Tamagawa number conjecture Reviewed International coauthorship

    David Burns, Masato Kurihara, Takamichi Sano

    ALGEBRA & NUMBER THEORY   11 ( 7 )   1527 - 1571   2017( ISSN:1937-0652

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    Publishing type:Research paper (scientific journal)   Kind of work:Joint Work  

    DOI: 10.2140/ant.2017.11.1527

  • On zeta elements for G_m Reviewed International coauthorship

    David Burns, Masato Kurihara, Takamichi Sano

    Documenta Mathematica   21   555 - 626   2016

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    Publishing type:Research paper (scientific journal)   Kind of work:Joint Work  

  • On a conjecture for Rubin-Stark elements in a special case Reviewed

    Tokyo Journal of Mathematics   38 ( 2 )   459 - 476   2015

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    Publishing type:Research paper (scientific journal)   Kind of work:Single Work  

  • Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns Reviewed

    Compositio Mathematica   150   1809 - 1835   2014

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    Publishing type:Research paper (scientific journal)   Kind of work:Single Work  

  • A generalization of Darmon's conjecture for Euler systems for general p-adic representations Reviewed

    Journal of Number Theory   144   281 - 324   2014

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    Publishing type:Research paper (scientific journal)   Kind of work:Single Work  

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MISC

  • A new conjecture for Rubin-Stark elements and its applications Reviewed

    RIMS Kokyuroku Bessatsu   B53   157 - 173   2015

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    Publishing type:Article, review, commentary, editorial, etc. (bulletin of university, research institution)   Kind of work:Single Work  

Presentations

  • On derivatives of Euler systems for motives Invited International conference

    Takamichi Sano

    Development of Iwasawa theory  2024.07 

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    Venue:Keio University  

  • On descent theory for Selmer complexes and applications to p-adic Birch and Swinnerton-Dyer conjectures Invited International conference

    Takamichi Sano

    Recent Progress on Hilbert’s 12th Problem  2024.06 

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    Venue:Edinburgh  

  • Selmer complexes and p-adic Birch and Swinnerton-Dyer conjectures Domestic conference

    Takamichi Sano

    Algebraic Number Theory and Related Topics 2023  2023.12 

  • Derived Bockstein maps and anticyclotomic p-adic Birch and Swinnerton-Dyer conjectures Invited International conference

    Takamichi Sano

    Arithmetic of L-functions  2023.05 

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    Presentation type:Oral presentation (invited, special)  

    Venue: ICMAT  

  • Hilbertの第12問題への応用 Invited Domestic conference

    佐野昂迪

    Dasgupta Kakdeの最近の仕事とその周辺Workshop  2022.02 

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    Presentation type:Oral presentation (general)  

    Venue:慶應義塾大学  

  • Recent progress on Hilbert’s 12th problem Invited International conference

    Takamichi Sano

    Algebraic Number Theory and Related Topics 2021  2021.12 

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    Presentation type:Oral presentation (invited, special)  

    Venue:Research Institute for Mathematical Sciences, Kyoto University  

  • On derivatives of Kato's Euler system and the Mazur-Tate Conjecture Invited International conference

    Takamichi Sano

    Number Theory Seminar  2021.05 

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    Presentation type:Oral presentation (general)  

    Venue:Yanqi Lake Beijing Institute of Mathematical Sciences and Applications  

  • On the equivariant Tamagawa number conjecture Invited Domestic conference

    Takamichi Sano

    2020.12 

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    Presentation type:Oral presentation (general)  

  • On a generalization of Perrin-Riou's conjecture on Kato's zeta elements Invited International conference

    Takamichi Sano

    Number Theory Seminar  2020.02 

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    Presentation type:Oral presentation (general)  

    Venue:The University of Cambridge  

  • On the local Tamagawa number conjecture and functional equations of Euler systems Invited International conference

    Takamichi Sano

    KAH-INI Seminar  2020.01 

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    Presentation type:Oral presentation (general)  

    Venue:Isaac Newton Institute  

  • On functional equations of Euler systems Invited International conference

    Takamichi Sano

    Number Theory Seminar  2019.12 

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    Presentation type:Oral presentation (general)  

    Venue:Autonomous University of Madrid  

  • Tamagawa number conjecture and Iwasawa theory Invited International conference

    Takamichi Sano

    Algebra and Number Theory Seminar  2019.11 

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    Presentation type:Oral presentation (general)  

    Venue:University College Dublin  

  • On a generalization of Perrin-Riou's conjecture on Kato's zeta elements Invited International conference

    Takamichi Sano

    Recent advances in the arithmetic of Galois representations  2019.07 

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    Presentation type:Oral presentation (general)  

    Venue:University of Genova  

  • On a new conjecture on Kato's zeta elements Invited International conference

    Takamichi Sano

    Oberseminar  2019.07 

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    Presentation type:Oral presentation (general)  

    Venue:LMU Munich  

  • Recent developments on Stark-type conjectures Invited International conference

    Takamichi Sano

    Algebraic Number Theory and Related Topics 2017  2017.12 

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    Presentation type:Oral presentation (general)  

  • Generalized Stark elements and p-adic L-functions Invited International conference

    Takamichi Sano

    Workshop on p-adic L-functions and algebraic cycles  2017.09 

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    Presentation type:Oral presentation (general)  

  • Recent developments on the theory of Euler systems Invited Domestic conference

    Takamichi Sano

    The 62nd Algebra Symposium  2017.09 

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    Presentation type:Oral presentation (general)  

  • Generalized Stark elements of arbitrary weights for G_m Invited International conference

    Takamichi Sano

    Iwasawa 2017  2017.07 

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    Presentation type:Oral presentation (general)  

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Grant-in-Aid for Scientific Research

  • ゼータ元の多角的研究

    Grant-in-Aid for Early-Career Scientists  2026

  • ゼータ元の多角的研究

    Grant-in-Aid for Early-Career Scientists  2025

  • New Development of Iwasawa theory and Euler systems

    Grant-in-Aid for Scientific Research(B)  2025

  • ゼータ元の多角的研究

    Grant-in-Aid for Early-Career Scientists  2024

  • New Development of Iwasawa theory and Euler systems

    Grant-in-Aid for Scientific Research(B)  2024

  • ゼータ元の多角的研究

    Grant-in-Aid for Early-Career Scientists  2022

  • 岩澤理論とオイラー系理論の新展開

    Grant-in-Aid for Scientific Research(B)  2022

  • 同変玉河数予想と高階岩澤理論の研究

    Grant-in-Aid for Young Scientists(B)  2017.04

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Charge of on-campus class subject

  • 代数学1演習

    2024   Weekly class   Undergraduate

  • 代数学1

    2024   Weekly class   Undergraduate

  • 数学特別研究2A

    2024   Intensive lecture   Graduate school

  • 数学特別研究1A

    2024   Intensive lecture   Graduate school

  • 数理構造論演習1

    2024   Intensive lecture   Graduate school

  • 数学概論B

    2024   Weekly class   Graduate school

  • 数学特別研究5A

    2024   Intensive lecture   Graduate school

  • 数学特別研究4A

    2024   Intensive lecture   Graduate school

  • 数学特別研究3A

    2024   Intensive lecture   Graduate school

  • 基礎数学A

    2024   Weekly class   Graduate school

  • 線形代数1

    2023   Weekly class   Undergraduate

  • 基礎数学A

    2023   Weekly class   Undergraduate

  • 線形代数2A

    2023   Weekly class   Undergraduate

  • 線形代数2A

    2023   Weekly class   Undergraduate

  • 基礎数学B

    2023   Weekly class   Undergraduate

  • 基礎数学A

    2022   Weekly class   Undergraduate

  • 数学概論B

    2022   Weekly class   Graduate school

  • 数学基礎演習1

    2022   Weekly class   Undergraduate

  • 代数学特論C

    2022   Weekly class   Graduate school

  • 代数学講義IV

    2022   Weekly class   Undergraduate

  • 基礎数学B/必:経,選:商<商・公>3(市大:CE1c)S

    2022   Weekly class   Undergraduate

  • 線形代数2A/必:理<物理>(市大:S1物・T1電機情)S

    2022   Weekly class   Undergraduate

  • 代数学IV

    2020     Undergraduate

  • 数学基礎演習II

    2020     Undergraduate

  • 解析II

    2020     Undergraduate

  • 代数学III

    2018     Undergraduate

  • 数学基礎演習I

    2018     Undergraduate

  • 基礎数学A

    2018     Undergraduate

  • 代数学特論III

    2017     Graduate school

  • 数学基礎演習II

    2017     Undergraduate

  • 解析I

    2017     Undergraduate

  • 基礎数学A

    2017     Undergraduate

  • 代数学特論IV

    2016     Graduate school

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Social Activities ⇒ Link to the list of Social Activities

  • オープンキャンパス2018

    Role(s): Lecturer

    Type: Lecture

    2018.08

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    Audience: High school students

  • 数学や理科の好きな高校生のための市大授業

    Role(s): Lecturer

    Type: Lecture

    2017.04

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    Audience: High school students