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

Frobenius态射和代数几何正特征直接像的稳定性

• 批准号: 22740017
• 负责人: KITADAI Yukinori
• 金额: $ 2.66万
• 依托单位: Hiroshima Institute of Technology (2011-2013)Hiroshima University (2010)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740017/
• 关键词: 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

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.

本文研究了半稳定向量丛在正特征代数簇上的Frobenius态射直接象是否保持其半稳定性及相关问题。 计算了余切丛是半稳定的代数曲面和非半稳定的代数曲面。 另外，作为代数在正特征上的应用，研究了利用Artin-Schreier塔的伪随机数发生器AST及其性质。

项目成果

A pseudorandom number generator using an Artin-Schreier tower (a joint work with Song Huiling and Hiroyuki Ito)

使用 Artin-Schreier 塔的伪随机数生成器（与宋惠玲和 Hiroyuki Ito 合作）

• 发表时间: 2014
• 作者: Inaba;Michi-aki;Craig Pastro;榎本直也;北臺如法
• 通讯作者: 北臺如法

A pseudorandom number generator using an Artin-Schreier tower

使用 Artin-Schreier 塔的伪随机数生成器

• 发表时间: 2011
• 期刊: SUT Journal of Mathematics
• 作者: Huiling Song;Hiroyuki Ito and Yukinori Kitadai
• 通讯作者: Hiroyuki Ito and Yukinori Kitadai