Matteo Montagnani (Mainz): Geometric properties of analytic categories of sheaves

Geometric properties of analytic categories of sheaves

 In algebraic geometry, it is a well-established practice to study geometric properties of algebraic varieties through the study of certain categories of sheaves. For instance, smooth algebraic varieties can be intrinsically characterized using Kontsevich's notion of a smooth category. In this talk, we discuss the key obstacles to adapting this categorical perspective to analytic geometry, where classical sheaf-theoretic and tensor-product operations are not well-behaved. We then show how the framework of condensed mathematics, introduced by Clausen and Scholze, can be used to categorically characterize geometric properties of (rigid) analytic spaces.