Simpson gerbe and p-adic nonabelian Hodge theory
组织者
刁晗生
, 杜衡
, 胡悦科
, Bin Xu
, Yihang Zhu
演讲者
Mingjia Zhang
时间
2024年10月14日 09:00 至 10:00
地点
Online
线上
Zoom 455 260 1552
(YMSC)
摘要
For a smooth proper rigid space $X$ over a complete algebraic closure $C$ of $Q_p$, Faltings observed that there is a p-adic analogue of the Corlette-Simpson correspondence, relating generalized representations of its etale fundamental group and Higgs bundles on it. He established an equivalence between the two categories in the case $X$ is a curve, which is recently extended to general $X$'s by Ben Heuer. Inspired by the work of Heuer, we observe that over the (Tate-twisted) cotangent bundle of $X$, there is a canonical etale $G_m$ -gerbe (which we call Simpson gerbe), whose coherent sheaf theory provides a clean interpretation of this equivalence. This talk will explain this perspective. Everything is joint work in progress with Bhargav Bhatt.