Simpson gerbe and p-adic nonabelian Hodge theory
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Mingjia Zhang
Time
Monday, October 14, 2024 9:00 AM - 10:00 AM
Venue
Online
Online
Zoom 455 260 1552
(YMSC)
Abstract
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.