Updated on 2024/10/09

写真a

 
SATO Kanetomo
 
Organization
Faculty of Science and Engineering Professor
Other responsible organization
Mathematics Course of Graduate School of Science and Engineering, Master's Program
Mathematics Course of Graduate School of Science and Engineering, Doctoral Program
Contact information
The inquiry by e-mail is 《here》
Homepage
https://c-research.chuo-u.ac.jp/html/100003154_ja.html?k=%E4%BD%90%E8%97%A4%E5%91%A8%E5%8F%8B
External link

Degree

  • Ph.D (Mathematical Sciences) ( The University of Tokyo )

  • 修士(数理科学) ( 東京大学 )

Education

  • 1998.3
     

    The University of Tokyo   Graduate School of Mathematical Sciences   doctor course   completed

  • 1996.3
     

    The University of Tokyo   Graduate School of Mathematical Sciences   master course   completed

  • 1994.3
     

    The University of Tokyo   Faculty of Science   graduated

  • 1989.3
     

    愛知県私立滝高等学校   graduated

Research History

  • 2011.4 - Now

    Professor, Faculty of Science and Engineering, Chuo University

  • 2007.4 - 2011.3

    "Associate Professor, Graduate School of Mathematical Sciences, Nagoya University"   Graduate School of Mathematics

  • 2000.4 - 2007.3

    "Research Associate, Graduate School of Mathematical Sciences, Nagoya University"   Graduate School of Mathematics

  • 2003.10 - 2004.9

    Research Fellow supported by EPSRC (The University of Nottingham)

  • 2001.10 - 2003.9

    JSPS Postdoctoral Fellowship for Reseach Abroad

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Professional Memberships

  • 日本数学会

Research Interests

  • Algebraic K-groups

  • Arithmetic Geometry

  • Number Theory

  • Algebraic Cycles

  • Cohomology

Research Areas

  • Natural Science / Algebra  / Arithmetic Geometry

  • Natural Science / Algebra  / 代数学

Papers

  • Étale cohomology of arithmetic schemes and zeta values of arithmetic surfaces Reviewed

    Kanetomo Sato

    Journal of Number Theory   227   JNT Prime 166 - 234   2021.10

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • On p-adic vanishing cycles of log smooth families Reviewed

    Shuji SAITO, Kanetomo SATO

    Tunisian Journal of Mathematics   2   309 - 335   2020.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Mathematical Sciences Publishers  

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  • Étale duality for constructible sheaves on arithmetic schemes Reviewed

    Uwe JANNSEN, Shuji SAITO, Kanetomo SATO

    Journal für die Reine und angewandte Mathematik   688   1 - 65   2014.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：WALTER DE GRUYTER GMBH  

    In this note we relate the following three topics for arithmetic schemes: a general duality for etale constructible torsion sheaves, a theory of etale homology, and the arithmetic complexes of Gersten-Bloch-Ogus type defined by K. Kato (1986).
    In brief, there is an absolute duality using certain dualizing sheaves on these schemes, we describe and characterize the dualizing sheaves to some extent, relate them to symbol maps, define etale homology via the dualizing sheaves, and show that the niveau spectral sequence for the latter, constructed by the method of Bloch and Ogus (1974), leads to the complexes defined by Kato. Some of these relations may have been expected by experts, and some have been used implicitly in the literature, although we do not know any explicit reference for statements or proofs. Moreover, the main results are used in a crucial way in a paper by Jannsen and Saito (2003). So a major aim is to fill a gap in the literature, and a special emphasis is on precise formulations, including the determination of signs. But the general picture developed here may be of interest itself.

    DOI： 10.1515/crelle-2012-0043

    Web of Science

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  • Syntomic cohomology and Beilinson's Tate conjecture for K2 Reviewed

    Masanori ASAKURA, Kanetomo SATO

    Journal of Algebraic Geometry   22   481 - 547   2013

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    Language：English   Publishing type：Research paper (scientific journal)  

    We study Beilinson's Tate conjecture for K2 using the theory of syntomic cohomology. As an application, we construct integral indecomposable elements of K1 of elliptic surfaces. Moreover, we give the first example of a surface X with pg≠0 over a p-adic field such that the torsion of CH0(X) is finite. © 2013 University Press, Inc.

    DOI： 10.1090/S1056-3911-2012-00591-8

    Scopus

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  • Finiteness theorem for zero-cycles over p-adic fields Reviewed

    Shuji SAITO, Kanetomo SATO

    Annals of Mathematics   172   1593 - 1639   2010.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ANNAL MATHEMATICS  

    Let R be a henselian discrete valuation ring. Let X be a regular projective flat scheme over Spec (R) with generalized semistable reduction. We prove a bijectivity theorem for etale cycle class maps of the Chow group of 1-cycles on X. As an application, we prove a finiteness theorem for the Chow group of 0-cycles on a projective smooth variety over a p-adic field.

    DOI： 10.4007/annals.2010.172.1593

    Web of Science

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Books

  • 代数的サイクルとエタールコホモロジー

    斎藤秀司, 佐藤周友（ Role： Joint author）

    丸善出版  2012.12 

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    Total pages：672   Responsible for pages：580   Language：Japanese   Book type：Scholarly book

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Presentations

  • Étale cohomology of arithmetic surfaces and a zeta value Invited

    Kanetomo SATO

    2022.7 

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    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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  • 算術的曲面のエタールコホモロジーとゼータ値 Invited

    佐藤周友

    談話会  ( 東北大学大学院理学研究科（オンライン開催） )   2020.10  東北大学大学院理学研究科

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • 算術的曲面のエタールコホモロジーとゼータ関数の値 Invited

    佐藤周友

    第65回代数学シンポジウム  ( 千葉大学理学部（オンライン開催） )   2020.9  千葉大学理学部（オンライン開催）

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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  • \'Etale cohomology and a zeta-value of arithmetic schemes Invited

    Kanetomo SATO

    Rational Points on Higher Dimensional Varieties  ( RIMS, Kyoto )   2019.12 

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    Language：English  

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  • \'Etale cohomology and a zeta value of arithmetic surfaces Invited

    Kanetomo SATO

    京都大学談話会  ( 京都大学数理解析研究所, 京都市左京区 )   2019.11  京都大学大学院理学研究科, 数理解析研究所

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

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Awards

  • 2018年度日本数学会代数学賞

    2018.3   日本数学会   数論的スキームに対する新しいコホモロジー理論とその応用

    佐藤周友

  • 2001年度日本数学会賞建部賢弘奨励賞

    2001.10   日本数学会   数体上の多様体のサイクル写像

    佐藤周友

Research Projects

  • 代数的サイクルを用いたゼータ関数の研究

    2020.4 - 2025.3

    文部科学省  科学研究費補助金  基盤研究(C) 

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    Grant type：Competitive

    Grant amount： \4550000 （ Direct Cost: \3500000 、 Indirect Cost： \1050000 ）

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  • Motivic cohomology over discrete valuation rings

    Grant number：23340004  2011.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B) 

    Geisser Thomas, Hesselholt Lars, Saito Shuji, Sato Kanetomo, Asakura Masanori

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    Grant amount： \17680000 （ Direct Cost: \13600000 、 Indirect Cost： \4080000 ）

    Arithmetic geometry is the study of integral or rational solutions of systems of polynomial equations. For this, it is often useful to study the solutions in other domains, like complex number, real numbers, finite fields, or p-adic fields. An important invariant of such solution sets are motivic cohomology, higher Chow groups, and Suslin homology. During this project, I studied these invariants, and proved several interesting results about them.

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  • Algebraic Cycles and Higher Abel-Jacobi map

    Grant number：14340009  2002 - 2005

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B) 

    SAITO Shuji, SAITO Takeshi, KATSURA Toshiyuki, MIYAOKA Yoichi

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    Grant amount： \9900000 （ Direct Cost: \9900000 ）

    Motivic cohomology is one of the most significant objects to study in arithmetic and algebraic geometry. For example, let K be a number field and O_K be its ring of integers. Then the ideal class group of K and the group of units in O_K are motivic cohomology of the scheme Spec(O_K).
    An important conjecture in arithmetic geometry is finiteness of motivic cohomology of arithmetic schemes. This is a natural generalization of the finiteness result for the above examples, which is a fundamental fact in classical number theory. There have been very few results on the problem so far except the case of Spec(O_K) or a curve over a finite field.
    In our research we have proved a new finiteness result for motivic cohomology. To state a result, let X be either regular projective flat over Spec(O_K) (arithmetic case) or a projective smooth variety over a finite field F (geometric case). The first crucial observation is that the finiteness of a certain motivic cohomology of X follows from a conjecture of Kato on the vanishing of KH_q(X) for integers q〓1. Here KH_q(X) is a certain arithmetic invariant attached to X. The Kato conjecture in case X=Spec(O_K) is equivalent to a fundamental fact in number theory concerning the Brauer group of K, which implies the Hasse principle for central simple algebras over K.
    We have shown the Kato conjecture in geometric case under the assumption of resolution of singu-larities. To be more precise we have obtain the following:
    Theorem Let X be a projective smooth variety over a finite field. Let γ〓1 be an integer. Assume resolution of singularities for subvarieties of dimension〓_K embedded in a smooth variety over F. Then KH_q(X)=0 for 1〓q〓γ+2.
    We have also succeeded to show the resolution of singularities in the above sense in case γ=2. Thus we get KH_q(X)=0 for 1〓q〓4 unconditionally and it gives rise to a new finiteness result for motivic cohomology of X.

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  • 数体上の代数多様体のモチビックコホモロジー群

    Grant number：13740007  2001 　 　

    日本学術振興会  科学研究費助成事業  奨励研究(A)  名古屋大学

    佐藤 周友

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    Grant amount： \1000000 （ Direct Cost: \1000000 ）

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  • 半安定還元をもつ代数多様体のCHOW群のねじれ部分の有限性とサイクル写像の単射性

    Grant number：96J04303  1998 　 　

    日本学術振興会  科学研究費助成事業  特別研究員奨励費  東京工業大学

    佐藤 周友

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    Grant amount： \800000 （ Direct Cost: \800000 ）

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Teaching Experience

  • 数学特殊論文研修 VI

  • 数学特殊論文研修 V

  • 数学特殊論文研修 IV

  • 数学特殊論文研修 III

  • 数学特殊論文研修 II

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Committee Memberships

  • 2024.6 - Now

    日本数学会   理事  

  • 2023.7 - Now

    日本数学会   雑誌`数学'編集委員長  

  • 2023.3 - Now

    日本数学会   評議員（編集会）  

  • 2022.3 - 2023.2

    日本数学会   代議員（関東支部第6ブロック選出）  

  • 2020.3 - 2021.2

    日本数学会   『数学通信』非常任編集委員  

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