报告人简介

张磊，博士毕业于德国杜伊斯堡-埃森大学，导师为H´el`ene Esnault教授，现任中山大学（珠海校区）数学科学学院副教授。研究方向为数论与算术几何，相关研究发表于J.Alg.Geom.,Math.Ann.,Trans.Amer.Math.Soc. 等知名数学期刊。

内容简介

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. There is a natural morphism from the pro-étale fundamental group to the étale fundamental group which realizes the étale fundamental group as the profinite completion of the pro-étale fundamental group. However, there has been no direct comparison between the topological and pro-étale fundamental groups. In this talk, we are going to present this comparison. We'll also introduce some comparison theorems in the p-adic setting.