Arithmetic geometric approach for period integrals

从代数对应、代数循环和自同构函数等特殊函数的角度研究了代数变量的周期积分。将棒状构造方法应用于正特征基域上的代数变体，描述了它们的p-基群，并利用Deligne微分梯度代数建立了Hodge实现函子的基本工具。我们还证明了关于混合椭圆动机的部分贝林森猜想。关于自同构函数，我们建立了与K3曲面等相关的几个新的Thomae型定理。

We study period integrals of algebraic varieties from the view point of algebraic correspondence, algebraic cycles and special functions such as automorphic functions. By applying the method of bar construction to algebraic varieties over positive characteristic base field, we describe their p-fundamental group, and establish a basic tools for Hodge realization functors using Deligne differential graded algebras. We also prove some part of Beilinson conjectures concerning mixed elliptic motives. Concerning automorphic functions, we stablish several new Thomae type theorems related to K3 surfaces, etc.