Pointwise good reduction criteria for local systems
Dr. Ziquan Yang
2024-06-26 16:00-17:00
MCM110
Speaker: Dr. Ziquan Yang (The Chinese University of Hong Kong)Time: 16:00-17:00 June 26, 2024 (Wednesday)
Venue: MCM110
Title: Pointwise good reduction criteria for local systems
Abstract: Let S be a connected smooth rigid analytic variety over a p-adic field K and let T be a p-adic local system over S. There are two fundamental results which tell us when T is de Rham: Scholze proved that the relative p-adic cohomology of a smooth and proper family over S is de Rham. Liu and Zhu proved that if T is de Rham at one classical point, then T is so everywhere.
In this talk, I will present a recent work with Haoyang Guo which aims to extend the above results to crystalline and semi-stable local systems. Our approach focuses on identifying the correct analogue of Liu-Zhu's theorem. Namely, if S admits a smooth (resp. semi-stable) integral model, then T is crystalline (resp. semi-stable) provided that it is so at "sufficiently many" classical points. Then I will explain how this can be used to extend Scholze's theorem. Time permitting, I will give a sketch of the proof.
