In this talk I will explain a computation that we did with Damien Junger, in which we determined the étale cohomology with \(\mathbb G_m\) 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 \(\mathbb G_m\) from its stalks. Instead we consider the quotient \(\mathbb G_m/U\) 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.
\(\mathbb G_m\)-cohomology of \(p\)-adic Stein spaces
14.04.2026 13:15 - 14:45
Organiser:
H. Grobner, A. Mellit, A. Minguez, B. Szendroi
Location: