Geometry Seminar

I will explain how to obtain a six-functor formalism (in the sense of Mann) for quasi-coherent sheaves on (derived) rigid-analytic varieties. The underlying functional analysis uses bornological spaces and a recently developed theory of derived analytic geometry due to Ben-Bassat--Kelly--Kremnitzer. Then, I will explain how to use this to obtain a six-functor formalism for crystals on these derived rigid spaces. This work is similar in spirit to work of Rodríguez Camargo and inspired by work of Andy Jiang. Time permitting, I may explain a relation to the theory of D-cap modules developed by Ardakov and Wadsley.