Séminaire de Mathématique

The pro-étale topology

by Prof. Bhargav BHATT (IAS & IHÉS)

Amphitéâtre Léon Motchane (IHES)

Amphitéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
I will discuss joint work with Peter Scholze on the pro-étale topology of schemes. The main goal of this work is to give an intuitive perspective on the foundations of l-adic cohomology. After giving the basic definitions, I will explain the local contractibility of the pro-étale site of a scheme (and its homological consequences). Using this, we will see why the category of locally constant sheaves on the pro-étale topology gives rise to a fundamental group that is rich enough to detect all lisse l-adic sheaves through its representation theory (which fails for the groups constructed in SGA1 and SGA3 on non-normal schemes).