|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||Cohomology of $p$-adic Stein spaces|
|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.