# Cohomology of $p$-adic Stein spaces

 Joint IAS/Princeton University Number Theory Seminar Topic: Cohomology of $p$-adic Stein spaces Speaker: Wieslawa Niziol Affiliation: École normale supérieure de Lyon Date: Thursday, September 21 Time/Room: 4:30pm - 5:30pm/Fine 214, Princeton University

I will discuss a comparison theorem that allows us to recover $p$-adic (pro-)etale cohomology of $p$-adic Stein spaces with semistable reduction over local rings of mixed characteristic from complexes of differential forms. To illustrate possible applications, I will show how it allows us to compute cohomology of Drinfeld half-space in any dimension and of its coverings in dimension one. This is a joint work with Pierre Colmez and Gabriel Dospinescu.