MPI-Oberseminar jointly with **"Arithmetic Geometry, A conference in Honor of Hèléne Esnault on the occasion of Her 70th Birthday" at IHES:**

https://indico.math.cnrs.fr/event/11114/

**Abstract:** Prismatic cohomology is a unifying p-adic cohomology of p-adic formal schemes. Motivated by questions on locally analytic representations of p-adic groups and the p-adic Simpson correspondence, an extension of prismatic cohomology to rigid-analytic spaces (over Q_p or over F_p((t))) has been sought. We will explain what form this should take, and our progress on realizing this picture. This includes a degeneration from the analytic Hodge-Tate stack underlying the p-adic Simpson correspondence to a similar (analytic) stack related to the Ogus-Vologodsky correspondence in characteristic p. This is joint work in progress with Johannes Anschütz, Arthur-César le Bras and Juan Esteban Rodriguez Camargo.

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