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De Rham F-gauges and Shimura varieties

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

Xu Shen

时间

2024年05月13日 10:00 至 11:00

地点

Shuangqing-B627

摘要

We will talk about the notion of de Rham F-gauges, which are roughly enhanced coefficient objects for de Rham cohomology of smooth algebraic varieties in characteristic p. More precisely, these involve flat vector bundles together with Hodge and conjugate filtrations, and Frobenius structures between the associated Higgs fields and p-curvatures. We will explain how they are related to some other mod p Hodge structures, such as p-torsion Fontaine-Laffaille modules and F-zips. Finally, we discuss some applications to the mod p geometry and cohomology of Shimura varieties, where these objects arise naturally.