Speaker: Prof. Liang Xiao ，BICMR

Title: Selected topics on cohomology of (phi, Gamma)-modules

Language: Chinese

Time & Venue: 2024.11.22 10:00-12:00 MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)

Abstract: In this introductory lecture, I will first briefly recall various versions of (phi, Gamma)-modules and the Herr complex that computes the cohomology of (phi, Gamma)-modules, which in turn can be indentified with the Galois cohomology. Then, I will explain a proof of the finiteness results of (phi, Gamma)-cohomology over rigid analytic space, due to Liu-Kedlaya, which greatly simplifies the argument in Kedlaya-Pottharst-Xiao. Towards the later part of the talk, I will switch to discuss the more mysterious psi operator, and explain how one might use it to construct explicitly the cocycles representing a cohomology class.