Seminar

In characteristic zero, the HKR theorem takes on a particularly nice form, allowing one to identify the S^1 action on the loop stack with the de Rham differential in a functorial manner.  One then uses this additional structure to define shifted symplectic structures, by interpreting closed p-forms as certain S^1- equivariant functions on the loop stack. In this talk I will discuss work in progress to construct a filtered version of the loop stack (valid in positive and mixed characteristic) which allows us to recover some extra structure. Much of this is joint work with M. Robalo and B. Toën.