学术报告（张磊 2024.11.22）

摘要：B. Bhatt and P. Scholze introduced the notion of the pro-étale fundamental group for a topologically Noetherian scheme X in their celebrated work "The pro-étale cohomology for schemes". This is a topological group that classifies the geometric covers of X. Under the Yoneda embedding, the geometric covers are identified with sheaves of sets which are locally constant sheaves for the pro-étale topology. In particular, the finite étale covers are geometric. Therefore, the pro-étale fundamental group refines Grothendieck's étale fundamental group which classifies only finite étale covers. In this talk, we will introduce some comparison theorems about the pro-étale fundamental group in the complex analytic and the p-adic settings. The techniques we are using here are h-descent of the étale site and dévisage.