Motivic Action on Coherent Cohomology of Hilbert Modular Varieties
Motivic Action on Coherent Cohomology of Hilbert Modular Varieties
复制标题
希尔伯特模簇相干上同调的动机作用
DOI：
10.1093/imrn/rnac126
复制
发表时间：
2022
影响因子：
1
通讯作者：
Horawa, Aleksander
中科院分区：
文献类型：
--
作者：
Horawa, Aleksander
我们提出了一个动机上同群对Hilbert模变体的相干上同的作用，推广了Venkatesh、Prasanna和Harris的猜想。用上同调模和上同调模两种方式来描述这种作用，并推测它们都可以提升为对上同调的积分系数作用。该猜想得到了Stark关于artin函数特殊值猜想的理论证据和基变情况下的数值证据的支持。
We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology moduloand over, and we conjecture that they both lift to an action on cohomology with integral coefficients. The conjecture is supported by theoretical evidence based on Stark’s conjecture on special values of Artin-functions and by numerical evidence in base change cases.