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

• Project/Area Number: 22740017
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Hiroshima 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: ¥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.

Research Products

• [Journal Article] A pseudorandom number generator using an Artin-Schreier tower (2011)
  • 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
  • Peer Reviewed
• [Journal Article] A pseudorandom number generator using an Artin-Schreier tower (2011)
  • Author(s): Huiling Song, Hiroyuki Ito, Yukinori Kitadai
  • Journal Title: SUT Journal of Mathematics Volume: 47 Pages: 73-90
  • NAID: 120006397962
  • 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
• [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
• [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
• [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
  • 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
  • Invited