论文标题
在Shimura品种上的特殊周期
Derived special cycles on Shimura varieties
论文作者
论文摘要
我采用来自派生的代数几何形状的方法，在整体模型上为特殊周期类别提供均匀的模量理论结构，许多霍奇类型的Shimura品种，包括单一，Quaternionic和正交Shimura品种。这些循环的所有所需特性，即使对于对应于库德拉对应下的退化傅立叶系数的人，也自然而然地遵循结构。我在这个一般框架中提出了库德拉的模块化猜想，并为其有效性提供了一些初步证据。
I employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on integral models many Shimura varieties of Hodge type, including unitary, quaternionic, and orthogonal Shimura varieties. All desired properties of these cycles, even for those corresponding to degenerate Fourier coefficients under the Kudla correspondence, follow naturally from the construction. I formulate Kudla's modularity conjectures in this general framework, and give some preliminary evidence towards their validity.
