Orateur
Description
We prove a Hochschild--Konstant--Rosenberg (HKR) theorem for arbitrary derived Deligne--Mumford (DM) stacks. To this aim, we introduce the notion of orbifold inertia stack of a derived DM stack; this supplies a derived enhancement of the classical inertia stack, which does not always coincide with the classical truncation of the free loop space. We show that, in characteristic $0$, given a derived DM stack, the shifted tangent bundle of its orbifold inertia stack is equivalent to its free loop space. As applications, we determine the Hochschild homology and Hochschild cohomology of interesting derived DM stacks, for instance, weighted projective lines, root stacks, quotients by algebraic groups, mapping stacks. This is joint work with Lie Fu, Mauro Porta and Nicolo Sibilla.