2013 Fiscal Year Final Research Report
Stability of direct images by Frobenius morphisms and algebraic geometry in positive characteristic
| Project/Area Number |
22740017
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Hiroshima Institute of Technology (2011-2013)
Hiroshima University (2010) |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| 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 |
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| 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.
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