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Finite Group Schemes and Normal Basis Problem

Research Project

Project/Area Number 26400024
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Suwa Noriyuki  中央大学, 理工学部, 教授 (10196925)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
KeywordsKummer理論 / group scheme / algebraic torus / torsor / Hopf代数 / Hopf-Galois理論 / Artin-Schreier理論 / 正規底 / Hopf-Galois拡大
Outline of Final Research Achievements

It is a main purpose of our research to study the inverse Galois problem, which is one of the most important in the Galois theory.
We discuss the inverse Galois problem with normal basis, concerning Kummer theories for algebraic tori not only over a field but also over a ring, in the framework of group schemes. The unit group scheme of a group algebra plays an important role in this article, as was pointed out by Serre <Groupes algebriques et corps de classes>. We also formulate the notion of cleft extensions in the Hopf-Galois theory in the framework of algebraic geometry. The unit group scheme of the algebra of a finite flat group scheme plays a key role.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (8 results)

All 2017 2016 2015 Other

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

  • [Journal Article] Kummer theories for algebraic tori and normal basis problem2017

    • Author(s)
      Noriyuki Suwa
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 39 Pages: 827-862

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Group algebras and normal basis problem2015

    • Author(s)
      Noriyuki Suwa
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 67 Pages: 495-505

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] Kummer theories for algebraic tori and Noether's problem2016

    • Author(s)
      諏訪紀幸
    • Organizer
      2016大分整数論研究集会
    • Place of Presentation
      大分大学
    • Year and Date
      2016-10-09
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Group algebras and normal basis problem2016

    • Author(s)
      諏訪紀幸
    • Organizer
      Hopf Algebras Conference in Tsukuba
    • Place of Presentation
      つくば国際会議センター
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Kummer theory for algebraic tori and normal basis problem2016

    • Author(s)
      諏訪紀幸
    • Organizer
      研究集会「Tokyo Journal of Mathematics 筱田記念号刊行に寄せて」
    • Place of Presentation
      上智大学
    • Year and Date
      2016-03-21
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 数III方式 Kummer theories for algebraic tori2015

    • Author(s)
      諏訪紀幸
    • Organizer
      2015大分整数論研究集会
    • Place of Presentation
      大分大学
    • Year and Date
      2015-09-01
    • Related Report
      2015 Research-status Report
    • Invited
  • [Remarks] 中央大学学術リポジトリ

    • URL

      http://ir.c.chuo-u.ac.jp/repository/search/item/md/rsp/p/

    • Related Report
      2016 Annual Research Report 2014 Research-status Report
  • [Remarks] 中央大学リポジトリ

    • URL

      http://ir.c.chuo-u.ac.jp/repository/search/item/md/rsp/p/

    • Related Report
      2015 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

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