G_m-cohomology of p-adic Stein spaces

par Sally Gilles

jeudi 24 sept. 2026, 14:00 → 19:00 Europe/Paris

In this talk I will explain a computation that we did with Damien Junger, in which we determined the étale cohomology with G_m coefficients of some p-adic analytic spaces. One difficulty is that rigid analytic spaces do not have enough points and it is not possible to deduce the global behavior of \G_m from its stalks. Instead we consider the quotient G_m/U of G_m by the group of principal units U. The cohomology of this quotient (in some cases) can then be computed by looking at what happens over a point, whereas the cohomology of U can be computed by passing to the pro-étale site, via p-adic methods.