Emanuel Reinecke - 15h45 - The crystalline comparison theorem via the prismatic site.

Given a smooth proper scheme over a p-adic ring of integers, the ́etale cohomology of the generic fiber can be related to the crystalline cohomology of the special fiber. In my talk, I will review this connection and some of the necessary background. Then I will present a new perspective involving the prismatic site, which lets us compare the two cohomology theories with general coefficients, in the relative setting, and allowing ramified base rings. Joint work with Haoyang Guo.