Online seminar, U. Haifa Topology & Geometry seminar on June 20, 2021
A recording of the talk is available here.
Topology & Geometry Seminar
Speaker: Devarshi Mukherjee, University of Göttingen
Topic: Dagger geometry and cyclic homology
Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Sunday, June 20, 2021
In this talk, I will explain how to extend overconvergent non-archimedean geometry to the realm of non-commutative geometry. Over the complex numbers, this means extending the algebra of smooth functions (resp. the modules of differential forms) on a manifold to arbitrary associative algebras (resp. Hochschild homology). The precise way to encode this generalisation is that the periodic cyclic homology of a smooth manifold coincides with de Rham cohomology. In overconvergent non-archimedean geometry, the right replacement for de Rham cohomology is rigid cohomology. We take several steps in the direction of proving that analytic cyclic homology is the non-commutative generalisation of rigid cohomology. Along the way, we discuss examples of non-commutative overconvergent algebras, such as algebras that arise from group actions on varieties. This is joint work with Guillermo Cortinas and Ralf Meyer.