报告题目：The Pro-étale Fundamental Group à la Bhatt-Scholze

报告时间：2024-11-01  16:00-17:00

报 告 人：张磊 副教授（中山大学珠海分校）

报告地点：理学院东北楼四楼报告厅（404）

Abstract: B. Bhatt and P. Scholzeintroduced the notion of the pro-étalefundamental group for a topologically Noetherian scheme X in their celebrated work "The pro-étalecohomologyfor schemes". This is a topological group that classifies the geometric covers of X. Under the Yonedaembedding, the geometric covers are identified with sheaves of sets which are locally constant sheaves for the pro-étaletopology. In particular, the finite étalecovers are geometric. Therefore, the pro-étalefundamental group refines Grothendieck'sétalefundamental group which classifies only finite étalecovers. There is a natural morphism from the pro-étalefundamental group to the étalefundamental group which realizes the étalefundamental group as the profinite completion of the pro-étalefundamental group. However, there has been no direct comparison between the topological and pro-étalefundamental groups. In this talk, we are going to present this comparison. We'll also introduce some comparison theorems in the p-adicsetting.