Abstract: Building on the work of Behrend and Fantechi who constructed virtual fundamental classes for Deligne-Mumford stacks we construct virtual classes for Artin stacks. Our methods make heavy use of Lurie’s ∞-mathematics and in some sense the main goal of the talk is to explain how Lurie’s technology offers conceptual clarifications and that one can in fact deduce concrete results from it.
Joint with Piotr Pstragowski.