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Research on algebraic cycles on arithmetic schemes

Research Project

Project/Area Number 20740008
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionChuo University (2010)
Nagoya University (2008-2009)

Principal Investigator

SATO Kanetomo  中央大学, 理工学部, 教授 (50324398)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords数論幾何学 / 代数学 / 整数論 / 数論的代数幾何 / 代数的サイクル / コホモロジー
Research Abstract

We study arithmetic properties, including finiteness, of the Chow group of 1-cycles on arithmetic schemes, especially regular semistable families on p-adic integer rings. The main tool in in this approach is the cycle class map to the etale cohomology. We derive properties of cycles by showing the injectivity and surjectivity of this cycle class map. In fact, we obtained a stong l-adic property of the 1-cycles in some quite general situation, and were able to compute the Chow group of 0-cycles on some special rational surface over a p-adic field.

Report

(5 results)
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (34 results)

All 2010 2009 2008 Other

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (22 results)

  • [Journal Article] A finiteness theorem for zero-cycles over p-adic fields2010

    • Author(s)
      SAITO Shuji, SATO, Kanetomo
    • Journal Title

      Ann. of Math

      Volume: 172 Pages: 1593-1639

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A p-adic regulator map and finiteness results for arithmetic schemes2010

    • Author(s)
      SAITO Shuji, SATO, Kanetomo
    • Journal Title

      Documenta Math. Extra Volume : Andrei Suslin's Sixtieth Birthday

      Pages: 525-594

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kanetomo A finiteness theorem for zero-cycles over p-adic fields.2010

    • Author(s)
      SAITO Shuji, SATO
    • Journal Title

      Ann.of Math. 172

      Pages: 1593-1639

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Kanetomo A p-adic regulator map and finiteness results for arithmetic schemes.2010

    • Author(s)
      SAITO Shuji, SATO
    • Journal Title

      Documenta Math.\ Extra Volume : Andrei A.Suslin's Sixtieth Birthday

      Pages: 525-594

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A finiteness theorem for zero-cycles over p-adic fields2010

    • Author(s)
      Shuji Saito, Kanetomo Sato
    • Journal Title

      Annals of Mathematics

      Volume: 172 Pages: 1593-1639

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A p-adic regulator map and finiteness results for arithmetic schemes2010

    • Author(s)
      Shuji Saito, Kanetomo Sato
    • Journal Title

      Documenta Mathematica

      Volume: Suslin記念号 Pages: 525-594

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] l-adic class field theory for regular local rings2009

    • Author(s)
      SATO, Kanetomo
    • Journal Title

      Math. Ann

      Volume: 344 Pages: 341-352

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kanetomo l-adic class field theory for regular local rings.2009

    • Author(s)
      SATO
    • Journal Title

      Math.Ann. 344

      Pages: 341-352

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] I-adic class field theory for regular local rings2009

    • Author(s)
      Kanetomo Sato
    • Journal Title

      Mathematische Annalen 344

      Pages: 341-352

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Syntomic cohomology and Beilinson's Tate conjecture for K_2

    • Author(s)
      Masanori Asakura, Kanetomo Sato
    • Journal Title

      Journal of Algebraic Geometry

      Volume: (未定 掲載決定済み)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A p-adic regulator and finiteness results for arithmetic schemes

    • Author(s)
      Shuji Saito, Kanetomo Sato
    • Journal Title

      Documenta Math.Suslin記念号 (未定)(掲載決定済み)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Beilinson's Tate conjecture for K 2 of elliptic surface : survey and example

    • Author(s)
      Masanori Asakura, Kanetomo Sato
    • Journal Title

      Proceedings of a conference at TIFR (未定)(掲載決定済み)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] On 1-cycle class maps over p-adic integer rings2010

    • Author(s)
      SATO, Kanetomo
    • Organizer
      International Workshop on Motives in Tokyo, Part6
    • Place of Presentation
      東京大学
    • Year and Date
      2010-12-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Kanetomo On 1-cycle class maps over p-adic integer rings.2010

    • Author(s)
      SATO
    • Organizer
      International workshop on motives in Tokyo, Part 6
    • Place of Presentation
      東京大学
    • Year and Date
      2010-12-13
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On 1-cycle class maps over p-adic integer rings2010

    • Author(s)
      Kanetomo Sato
    • Organizer
      International workshop on motives, Part 6
    • Place of Presentation
      東京大学
    • Year and Date
      2010-12-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the Chow groups of 0-cycles of varieties over p-adic fields2010

    • Author(s)
      佐藤周友
    • Organizer
      代数幾何学城崎シンポジウム
    • Place of Presentation
      城崎大会議館
    • Year and Date
      2010-10-26
    • Related Report
      2010 Final Research Report
  • [Presentation] On the Chow groups of 0-cycles of varieties over p-adic fields.2010

    • Author(s)
      佐藤周友
    • Organizer
      代数幾何学城崎シンポジウム
    • Place of Presentation
      城崎大会議館
    • Year and Date
      2010-10-26
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the image of p-adic regulator2010

    • Author(s)
      佐藤周友
    • Organizer
      数論幾何学ワークショップ2010
    • Place of Presentation
      沖縄県那覇市
    • Year and Date
      2010-08-06
    • Related Report
      2010 Final Research Report
  • [Presentation] On the image of p-adic regulator2010

    • Author(s)
      Kanetomo Sato
    • Organizer
      数論幾何学ワークショップ2010
    • Place of Presentation
      沖縄尚学高校(沖縄県那覇市)
    • Year and Date
      2010-08-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Syntomic cohomology and Beilinson's Tate conjecture for K^2(その2)2010

    • Author(s)
      佐藤周友
    • Organizer
      数論幾何学ワークショップ2010
    • Place of Presentation
      沖縄県那覇市
    • Year and Date
      2010-08-03
    • Related Report
      2010 Final Research Report
  • [Presentation] Syntomic cohomology and Beilinson's Tate conjecture for K^2(その1)2010

    • Author(s)
      佐藤周友
    • Organizer
      数論幾何学ワークショップ2010
    • Place of Presentation
      沖縄県那覇市
    • Year and Date
      2010-08-02
    • Related Report
      2010 Final Research Report
  • [Presentation] p進数体上の多様体の0 サイクルの有限性について2010

    • Author(s)
      佐藤周友
    • Organizer
      談話会
    • Place of Presentation
      広島大学
    • Year and Date
      2010-05-27
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] p進体上の多様体のチャウ群2010

    • Author(s)
      佐藤周友
    • Organizer
      整数論・保型形式セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2010-05-07
    • Related Report
      2010 Final Research Report
  • [Presentation] ガロアコホモロジー2009

    • Author(s)
      佐藤周友
    • Organizer
      整数論サマースクール
    • Place of Presentation
      京都市左京区
    • Year and Date
      2009-08-18
    • Related Report
      2010 Final Research Report
  • [Presentation] ガロアコホモロジー2009

    • Author(s)
      佐藤周友
    • Organizer
      第17回整数論サマースクール
    • Place of Presentation
      アピカルイン京都(京都市左京区)
    • Year and Date
      2009-08-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Higher cycle class maps for p-adic etale Tate twists2009

    • Author(s)
      SATO, Kanetomo
    • Organizer
      玉原数論幾何研究集会
    • Place of Presentation
      東大玉原国際セミナーハウス
    • Year and Date
      2009-05-26
    • Related Report
      2010 Final Research Report
  • [Presentation] Kanetomo Higher cycle class maps for p-adic etale Tate twists.2009

    • Author(s)
      SATO
    • Organizer
      玉原数論幾何研究集会
    • Place of Presentation
      東大玉原国際セミナーハウス
    • Year and Date
      2009-05-26
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Higher cycle class map for p-adic etale Tate twists2009

    • Author(s)
      Kanetomo Sato
    • Organizer
      玉原数論幾何研究集会
    • Place of Presentation
      東大玉原国際セミナーハウス
    • Year and Date
      2009-05-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 算術的スキームのp進的コホモロジーとサイクル写像2009

    • Author(s)
      佐藤周友
    • Organizer
      日本数学会代数学分科会特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] 算術的スキームのp進的コホモロジーとサイクル写像.2009

    • Author(s)
      佐藤周友
    • Organizer
      日本数学会代数学分科会特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Higher cycle class maps for p-adic etale Tate twists2008

    • Author(s)
      SATO, Kanetomo
    • Organizer
      研究集会「代数的K理論とmotive理論の現状」
    • Place of Presentation
      京大数理研
    • Year and Date
      2008-07-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Higher cycle class map for p-adic etale Tate twists2008

    • Author(s)
      Kanetomo Sato
    • Organizer
      代数的K理論とmotive理論の現状
    • Place of Presentation
      京大数理研
    • Year and Date
      2008-07-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] What is motive theory2008

    • Author(s)
      SATO, Kanetomo
    • Organizer
      研究集会「代数的K理論とmotive理論の現状」
    • Place of Presentation
      京大数理研
    • Year and Date
      2008-06-30
    • Related Report
      2010 Final Research Report
  • [Presentation] p進数体上の多様体の0サイクルの有限性について2008

    • Author(s)
      佐藤周友
    • Organizer
      談話会
    • Place of Presentation
      広島大学
    • Year and Date
      2008-05-27
    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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