论文标题
对希尔伯特模块化品种的相干共同体学的动机行动
Motivic action on coherent cohomology of Hilbert modular varieties
论文作者
论文摘要
我们提出了某个动机同谋小组对希尔伯特模块化品种的相干同谋的行动，扩展了Venkatesh，Prasanna和Harris的猜想。该动作以两种方式描述：关于同种学模型$ P $和$ \ Mathbb c $，我们认为它们都以积分系数为基础的共同体学。根据Stark对Artin $ l $ functions的特殊价值以及基本变化案例中的数值证据的猜想，理论证据支持了猜想。
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 modulo $p$ and over $\mathbb C$, 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 $L$-functions, and by numerical evidence in base change cases.
