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

研究了整权的Siegel模形式与半整权的Siegel模形式之间的对应关系，这与椭圆模形式上的Shimura对应关系相似。为此，我研究了上同调群的消失定理，使关于Jacobi形式空间维数的猜想成为一个定理。研究了用代数几何的方法计算Hecke算子的迹公式。

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.