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Categorification and geometry

Lars Hesselholt (IAS and Nagoya University)

Location:  Hill 705
Date & time: Wednesday, 21 February 2024 at 3:30PM - 4:30PM

Lars Hesselholt (IAS and Nagoya University)

Title: Categorification and 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 dualizably symmetric monoidal infinity-category be considered as the infinity-category of quasi-coherent modules on some geometric object. In this talk, I will explain this shift in paradigm as well as Clausen'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.