Algebra/Topology Seminar

Speaker: Shubhodip Mondal

Title: On p-adic de Rham cohomology

Abstract: In this talk, we will discuss an approach to de Rham cohomology in the p-adic context using group schemes and similar concrete structures, which we call G_a^{perf}-modules. As applications, I will mention the ``formal \'etaleness" property of the de Rham cohomology functor, which refines some earlier results obtained in the work of Bhatt-Lurie-Mathew and answers a question of Bhatt.

Time permitting, I will mention the connection between the G_a^{perf}-module approach with the stacky approach to p-adic de Rham cohomology due to Drinfeld and mention the classification of all the endomorphisms of de Rham cohomology functor and its application to the Deligne-Illusie decomposition obtained in joint work with Shizhang Li.