Speaker: Dr. Arnaud Vanhaecke ，MCM, CAS

Title: Cohomology of p-adic étale local systems on the coverings of Drinfeld's half plane

Language: Chinese 

Time & Venue: 2024.10.18 10:00-12:00  MCM110

Abstract: We explain how to extend the results of Colmez Dospinescu and Niziol to arbitrary Hodge-Tate weights. To achieve this, one needs to consider p-adic étale cohomology of the universal local system and its symmetric powers on Drinfeld's tower. The main observation is that these local systems are « isotrivial opers » on a curve, which allows for defining and computing their proétale cohomology. A striking difference with the trivial coefficient case is the appearance of potentially semi-stable 2-dimensional non-cristabelian Galois representations in the cohomology. After explaining how syntomic cohomology of isotrivial opers on a curve works, I will apply it to Drinfeld's universal local system and show how it relates to its étale cohomology before computing the multiplicities of Galois representations in it. Finally, I will sketch how to adapt the factorisation result of Colmez Dospinescu and Niziol to this case.