Group, Lie and Number Theory Seminar

Shimura varieties are certain varieties attached to a reductive group G whose geometry has been important in a wide range of applications. Notably, it is expected that their etale cohomology realizes the Langlands correspondence. Shimura varieties should be moduli spaces of certain motives with G-structure, and their cohomology should be closely related to the realizations of these motives in that cohomology theory.

Work of Bhatt and Scholze has shown that most cohomology theories are avatars of a single unifying theory: prismatic cohomology. I will discuss ongoing work with Naoki Imai and Hiroki Kato on the existence of a 'prismatic realization functor' for Shimura varieties of abelian type. This can be thought of as producing the prismatic cohomology realization of the motives with G structure that these Shimura varieties parameterize.
Speaker(s): Alex Youcis (University of Tokyo)