Talks (titles and abstracts)
Bhargav Bhatt: Integral p-adic Hodge theory
Given a smooth projective variety with good reduction over a p-adic field, in recent joint work with Morrow and Scholze, we constructed a cohomology theory that interpolates between the etale cohomology of the generic fiber and the crystalline cohomology of the special fiber integrally. This leads to concrete consequences such as: the mod p Betti numbers of the generic fiber are bounded above by the de Rham Betti numbers of the special fibre. In my talk, I'll recall this story, and then explain how to deduce analogous results in the semistable case using stacks. (This is joint work with Matthew Morrow and Peter Scholze.)
Gabriel Dospinescu: p-adic étale cohomology and the Drinfeld tower
Non abelian Lubin-Tate theory describes the l-adic cohomology of the Drinfeld tower in terms of local Langlands and Jacquet-Langlands correspondences. We will discuss a p-adic analogue (in dimension 1) of this picture, in which the p-adic local Langlands correspondence for GL_2(Q_p) naturally appears. This is joint work with Pierre Colmez and Wiesława Nizioł.
Kiran Kedlaya: Drinfeld's lemma and multivariate (phi, Gamma)-modules
In positive characteristic, the formation of profinite fundamental groups of schemes does not behave well with respect to products. However, it was observed by Drinfeld that this can be corrected by taking quotients by Frobenius. We show how the analogue of Drinfeld's lemma for perfectoid spaces can be used to construct multivariate (phi, Gamma)-modules associated to products of Galois groups of p-adic fields. Based on joint work with Annie Carter and Gergely Zábrádi.
Wiesława Nizioł: Cohomology of p-adic Stein spaces
I will describe how the geometric p-adic pro-etale cohomology of p-adic Stein spaces with semistable reduction can be recovered from their de Rham and Hyodo-Kato cohomologies. I will also discuss some examples. This is based on a joint work with Pierre Colmez and Gabriel Dospinescu.