2013 Fiscal Year Final Research Report
A Study of Shimura Correspondence on Siegel Modular Forms by a Method of Algebraic Geometry
| Project/Area Number |
23654016
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Meiji University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | ジーゲル保型形式 / ヤコビ形式 / 佐武コンパクト化 / トロイダル・コンパクト化 / リーマン・ロッホの定理 / 消滅定理 |
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| Research Abstract |
I studied a correspondence from Siegel modular forms of integral weight to Siegel modular forms of half integral weight which is similar to the Shimura correspondence on elliptic modular forms. For that purpose I studied the vanishing theorem of cohomology groups to make the conjecture on the dimension of the spaces of Jacobi forms a theorem. I also studied to compute a trace formula of Hecke operators by a method of algebraic geometry.
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