Simpson gerbe and p-adic nonabelian Hodge theory

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Mingjia Zhang (IAS)

Time：

Mon., 9:00-10:00 am, Oct. 14, 2024

Online：

Zoom Meeting ID: 4552601552

Passcode: YMSC

Title：

Simpson gerbe and p-adic nonabelian Hodge theory

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.