Number Theory Seminar

Speaker: Lucas Mann (Münster)

Title: 6-Functor Formalisms and the Category of Kernels

Abstract: 6-Functor formalisms provide a powerful tool for studying cohomology theories, and it turns out that the abstract theory of 6-functor formalisms is surprisingly rich. The main new idea, appearing in previous constructions by Lu-Zheng and Fargues-Scholze, is the 2-category of kernels associated with a 6-functor formalism. We present a systematic and rigorous study of this 2-category and explain how it conceptualizes many classical constructions in sheaf theories (such as étale and coherent sheaves) and representation theory, as well as providing new ones. This is joint work with Claudius Heyer.