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L-functions and motivic cohomology of arithmetic varieties and applications to cyclotomic fields

Research Project

Project/Area Number 25400007
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionChiba University

Principal Investigator

Otsubo Noriyuki  千葉大学, 大学院理学研究院, 准教授 (60332566)

Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsモチーフ / L関数 / モチーフ的コホモロジー / 超幾何関数 / 円分体 / レギュレーター / 周期 / フェルマー多様体 / 周期予想 / ヤコビ和 / 虚数乗法 / L関数 / イデアル類群
Outline of Final Research Achievements

We studied relations between L-functions of arithmetic varieties and their applications to cyclotomic fields. In particular, we obtained new relations between special values of Hecke L-functions of cyclotomic fields and motivic cohomology of Fermat motives, in terms of generalized hypergeometric functions. On the other hand, we defined a new class of families of varieties called hypergeometric fibrations, and for such families, proved the Gross-Deligne conjecture on periods and expressed the regulators in terms of generalized hypergeometric functions. Moreover, we determined the structure of the profinite homology of the tower of Fermat curves, and by using this, gave a simple construction of Ihara-Anderson's universal measure of Jacobi sums.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (22 results)

All 2018 2017 2016 2015 2014 2013 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 1 results,  Acknowledgement Compliant: 3 results) Presentation (15 results) (of which Int'l Joint Research: 5 results,  Invited: 7 results) Remarks (2 results)

  • [Journal Article] CM periods, CM regulators and hypergeometric functions, I2018

    • Author(s)
      Asakura Masanori、Otsubo Noriyuki
    • Journal Title

      canadian mathematical journal

      Volume: 70 (3) Issue: 3 Pages: 481-514

    • DOI

      10.4153/cjm-2017-008-6

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] CM periods, CM regulators and hypergeometric functions, II2017

    • Author(s)
      Masanori Asakura and Noriyuki Otsubo
    • Journal Title

      Math. Z.

      Volume: Online First Pages: 1-31

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Homology of the Fermat tower and universal measures for Jacobi sums2016

    • Author(s)
      Noriyuki Otsubo
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: 59 Issue: 3 Pages: 624-640

    • DOI

      10.4153/cmb-2016-012-0

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Homology of the Fermat tower and Universal Measures for Jacobi Sums2016

    • Author(s)
      Noriyuki Otsubo
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: 未定

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On Special Values of Jacobi-sum Hecke L-functions2015

    • Author(s)
      Noriyuki Otsubo
    • Journal Title

      Experimental Mathematcs

      Volume: 未定 Issue: 2 Pages: 247-259

    • DOI

      10.1080/10586458.2014.971199

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Regulators and hypergeometric functions2018

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      UK-Japan Winter School on Number Theory
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Regulators of hypergeometric fibrations2016

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      10th arithmetic and algebraic geometry
    • Place of Presentation
      東京大学(東京都・目黒区)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 虚数乗法を持つモチーフの周期とレギュレーターについて2016

    • Author(s)
      大坪紀之
    • Organizer
      熊本大学談話会
    • Place of Presentation
      熊本大学(熊本県・熊本市)
    • Related Report
      2016 Research-status Report
  • [Presentation] 超幾何ファイブレーションのK_1レギュレーター2016

    • Author(s)
      大坪紀之
    • Organizer
      第10回玉原特殊多様体研究集会熊本大学談話会
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県・沼田市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Complex multiplication and hypergeometric function超幾何ファイブレーションのK_1レギュレーター2016

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Japan-Taiwan joint conference on number theory
    • Place of Presentation
      Taiwan National University(台湾)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 虚数乗法を持つモチーフと超幾何関数2016

    • Author(s)
      大坪紀之
    • Organizer
      香川セミナー
    • Place of Presentation
      香川大学(香川県・高松市)
    • Related Report
      2016 Research-status Report
  • [Presentation] CM Periods, CM Regulators and Hypergeometric Functions2015

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Algebraic Geometry
    • Place of Presentation
      Indian Statistica Institute, Bangalore, India
    • Year and Date
      2015-12-14
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] CM Regulators and Hypergeometric Functions2015

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      The 5th East Asia Number Theory Conference
    • Place of Presentation
      Chuncheaon, Korea
    • Year and Date
      2015-08-26
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Period Conjecture of Gross-Deligne and a Regulator Formula for Fibrations with Complex Multiplication2015

    • Author(s)
      大坪紀之
    • Organizer
      整数論・保型形式セミナー
    • Place of Presentation
      大阪大学 (大阪府、豊中市)
    • Year and Date
      2015-05-29
    • Related Report
      2015 Research-status Report
  • [Presentation] CM regulators and hypergeometric functions2015

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      名古屋大学数論幾何セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2015-01-15
    • Related Report
      2014 Research-status Report
  • [Presentation] CM regulators, values of L-functions and hypergeometric functions2014

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Japan-Korea joint seminar on number theory and related tpics 2014
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2014-11-19 – 2014-11-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] CM periods, CM regulators and hypergeometric functions2014

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Workshop of arithmetic geometry in Tohoku
    • Place of Presentation
      東北大学
    • Year and Date
      2014-10-30 – 2014-10-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the Beilinson conjecture for Fermat motives2014

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      Number theory/representation theory seminar
    • Place of Presentation
      University of Toronto, Canada
    • Related Report
      2013 Research-status Report
  • [Presentation] Jacobi和の微分とBernoulli数の類似について2013

    • Author(s)
      大坪紀之
    • Organizer
      代数セミナー
    • Place of Presentation
      慶応大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Algebraic cycles and generalized hypergeometric functions2013

    • Author(s)
      Noriyuki Otsubo
    • Organizer
      GANITA Seminar
    • Place of Presentation
      University of Toronto, Canada
    • Related Report
      2013 Research-status Report
  • [Remarks] Noriyuki Otsubo's Home Page

    • URL

      http://www.math.s.chiba-u.ac.jp/~otsubo/

    • Related Report
      2017 Annual Research Report 2016 Research-status Report 2015 Research-status Report 2014 Research-status Report
  • [Remarks] Noriyuki Otsubo's Home Page

    • URL

      http://www.math.s.chiba-u.ac.jp/~otsubo/

    • Related Report
      2013 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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