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Algebraic cycles and motives with modulus for unipotent algebraic groups

Research Project

Project/Area Number 16K17579
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionJapan Women's University (2018-2021)
Tokyo Denki University (2016-2017)

Principal Investigator

SUGIYAMA Rin  日本女子大学, 理学部, 講師 (20633233)

Project Period (FY) 2016-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords相互層 / 加法群のテンソル積 / モジュラス付き代数的サイクル / 数論幾何 / modulus presheaf / tensor structure / motive with modulus / Chow group with modulus / Motive with modulus / 数論幾何学 / Cube invariant sheaves / Motives with modulus / 代数的サイクル / Reciprocity sheaves / 可換代数群 / モチーフ
Outline of Final Research Achievements

Tensor structures of reciprocity sheaves induced by tensor structures on the category of modulus sheaves with transfers were revealed. Using this I computed concretely the tensor products of the additive groups and the multiplicative groups as reciprocity sheaves. In particular, I computed the tensor product of two copies of the additive group. This is a completely new result, since the theory of motive using the homotopy invariance can not deal with that case.I also gave a description of the Chow group of 0-cycles with modulus for product of curves in terms of the tensor product of its Jacobian varieties.

Academic Significance and Societal Importance of the Research Achievements

代数多様体のモチーフに関する理論は盛んに研究され続けている理論であり、その中でホモトピー不変性を仮定しないモチーフ理論(モジュラス付きモチーフの理論)は近年発展しているものである。今回の研究成果は、ホモトピー不変でない最も基本的な対象である加法群について、新たな枠組みでの計算を行い、その構造を明らかにした。今後も関連する計算は、モジュラス付きモチーフの振る舞いを明らかにすることへ繋がると思われる。

Report

(7 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (11 results)

All 2021 2019 2018 2017 2016 Other

All Int'l Joint Research (4 results) Journal Article (2 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (5 results) (of which Int'l Joint Research: 1 results,  Invited: 5 results)

  • [Int'l Joint Research] ヴッパータール大学/ミュンヘン大学(ドイツ)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] ミラノ大学(イタリア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] FREIE UNIVERSITAET BERLIN(ドイツ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] The university of Milan(イタリア)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Tensor structures in the theory of modulus presheaves with transfers2021

    • Author(s)
      R?lling Kay、Sugiyama Rin、Yamazaki Takao
    • Journal Title

      Mathematische Zeitschrift

      Volume: 300 Issue: 1 Pages: 929-977

    • DOI

      10.1007/s00209-021-02819-2

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus2017

    • Author(s)
      Federico Binda, Jin Cao, Wataru Kai, Rin Sugiyama
    • Journal Title

      Journal of Algebra

      Volume: 469 Pages: 437-463

    • DOI

      10.1016/j.jalgebra.2016.07.036

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Tensor structures of modulus sheaves with transfers2021

    • Author(s)
      Rin Sugiyama
    • Organizer
      The 9th East Asia Number Theory Conference
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tensor products for cube-invariant sheaves2019

    • Author(s)
      杉山倫
    • Organizer
      ミラノ大学 セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Reciprocity 層のテンソル積の計算2018

    • Author(s)
      杉山倫
    • Organizer
      東京電機大学 数学講演会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Tensor product and K-group of geometric type for reciprocity sheaves2017

    • Author(s)
      杉山倫
    • Organizer
      Regulators in Niseko 2017
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] K-group of geometric type for reciprocity sheaves2016

    • Author(s)
      杉山倫
    • Organizer
      中央大学 代数セミナー
    • Place of Presentation
      中央大学(東京都文京区)
    • Year and Date
      2016-11-16
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2016-04-21   Modified: 2023-01-30  

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