Shimura varieties with infinite level, and torsion in the cohomology of locally symmetric spaces
(Université de Bonn)
Centre de conférences Marilyn et James Simons (IHES)
Centre de conférences Marilyn et James Simons
Le Bois Marie
35, route de Chartres
We will discuss the p-adic geometry of Shimura varieties with infinite level at p: They are perfectoid spaces, and there is a new period map defined at infinite level. As an application, we will discuss some results on torsion in the cohomology of locally symmetric spaces, and in particular the existence of Galois representations in this setup.