Emanuele Pavia: Sheaves of categories over topological and coaffine stacks скачать в хорошем качестве

Emanuele Pavia: Sheaves of categories over topological and coaffine stacks

Date: 27 March 2024 Abstract: Starting from any sufficiently nice topological space X, one can produce two different (derived) stacks defined over a field k of characteristic 0: the Betti stack X_B, which bears information on the underlying homotopy type of X, and the coaffine stack cSpec(C*(X; k)) on the commutative algebra C*(X; k) of k-valued singular cochains on X, which behaves as the affinization of the Betti stack X_B. In this talk, I shall apply the technical machinery of sheaves of (∞-)categories on derived stacks as developed in Gaitsgory’s work to the case of Betti stacks and their associated coaffine stacks. We shall see how sheaves of categories on X_B are intimately related to categorified local systems over the original space X and to homotopy-coherent actions of topological groups on k-linear ∞-categories. At the very end, I shall briefly describe how sheaves of categories on X_B and on cSpec(C*(X; k)) interact, and how such interaction can be interpreted as an instance of higher Koszul duality. This talk is based on upcoming joint work with J. Pascaleff and N. Sibilla. Slides: https://drive.google.com/file/d/1DGuv... Emanuele Pavia: https://emanuelepavia.com/ LAGOON Webinar: https://sites.google.com/view/lagoonw...