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Stability of direct images by Frobenius morphisms and algebraic geometry in positive characteristic

Research Project

Project/Area Number 22740017
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionHiroshima Institute of Technology (2011-2013)
Hiroshima University (2010)

Principal Investigator

KITADAI Yukinori  広島工業大学, 工学部, 助教 (30511563)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsベクトル束 / 安定性 / 半安定ベクトル束 / 正標数 / フロベニウス写像 / 疑似乱数 / 有限体 / Artin-Schreier拡大 / 代数幾何学 / 半安定余接束 / 小平消滅定理
Research Abstract

I studied the problem of whether taking direct images of semistable vector bundles on algebraic varieties in positive characteristic by Frobenius morphisms preserves thier semistability or not and related problems. Calculations to find concrete examples of algebraic surfaces whose cotangent bundles are semitable or are not semistable by Frobenius pullback several times were proceeded. In addition, I studied a pseudorandom number generator AST using an Artin-Schreier tower and its properties as an application of algebra in positive characteristic.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (7 results)

All 2014 2012 2011

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (5 results) (of which Invited: 2 results)

  • [Journal Article] A pseudorandom number generator using an Artin-Schreier tower2011

    • Author(s)
      宋慧玲, 伊藤浩行, 北臺如法
    • Journal Title

      SUT Journal of Mathematics

      Volume: 47巻, no.1 Pages: 73-90

    • NAID

      120006397962

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A pseudorandom number generator using an Artin-Schreier tower2011

    • Author(s)
      Huiling Song, Hiroyuki Ito, Yukinori Kitadai
    • Journal Title

      SUT Journal of Mathematics

      Volume: 47 Pages: 73-90

    • NAID

      120006397962

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] A pseudorandom number generator using an Artin-Schreier tower (a joint work with Song Huiling and Hiroyuki Ito)2014

    • Author(s)
      北臺如法
    • Organizer
      愛媛大学代数セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      2014-02-10
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] A pseudorandom number generator using an Artin-Schreier tower (a joint work with Song Huiling and Hiroyuki Ito)2012

    • Author(s)
      北臺如法
    • Organizer
      研究集会「射影多様体の幾何とその周辺2012」(高知研究集会)
    • Place of Presentation
      高知大学
    • Year and Date
      2012-10-07
    • Related Report
      2013 Final Research Report
  • [Presentation] A pseudorandom number generator using an Artin-Schreier tower (a joint work with Song Huiling and Hiroyuki Ito)2012

    • Author(s)
      北臺如法
    • Organizer
      Workshop on Galois point and related topics
    • Place of Presentation
      山形大学理学部1号館1階13番教室
    • Year and Date
      2012-09-16
    • Related Report
      2013 Final Research Report
  • [Presentation] A pseudorandom number generator using an Artin-Schreier tower (a joint work with Song Huiling and Hiroyuki Ito)2012

    • Author(s)
      北臺如法
    • Organizer
      Workshop on Galois point and related topics
    • Place of Presentation
      山形大学理学部1号館 1階13番教室
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] A pseudorandom number generator using an Artin-Schreier tower (a joint work with Song Huiling and Hiroyuki Ito)2012

    • Author(s)
      北臺如法
    • Organizer
      研究集会「射影多様体の幾何とその周辺2012」
    • Place of Presentation
      高知大学
    • Related Report
      2012 Annual Research Report
    • Invited

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Published: 2010-08-23   Modified: 2019-07-29  

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