A Study of Shimura Correspondence on Siegel Modular Forms by a Method of Algebraic Geometry

Research Project

Project/Area Number	23654016
Research Category	Grant-in-Aid for Challenging Exploratory Research
Allocation Type	Multi-year Fund
Research Field	Algebra
Research Institution	Meiji University
Principal Investigator	TSUSHIMA Ryuji 明治大学, 理工学部, 教授 (20118764)
Project Period (FY)	2011 – 2013
Project Status	Completed (Fiscal Year 2013)
Budget Amount *help	¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000) Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000) Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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 / 代数幾何学 / ヘッケ作用素
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.