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Le Bois Marie
35, route de Chartres
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).