Special Year Workshop on p-adic Arithmetic Geometry

Abstract: The key principle in Grothendieck's algebraic geometry is that every commutative ring be considered as the ring of functions on some geometric object. Clausen and Scholze have introduced a categorification of algebraic and analytic geometry, where the key principle is that every stable closed symmetric monoidal infinity-category be considered as the infinity-category of quasi-coherent modules on some geometric object. In this talk, I will expland on this principle as well as Scholze's philosophy that *every* cohomology theory should arise from this picture, complete with a six-functor formalism of categories of coefficients. The Hahn-Raksit-Wilson even filtration and Efimov continuity are key ingredients.