Choices of HKR isomorphisms

Abstract

In this short note we record the fact that the set of multiplicative HKR natural equivalences defined simultaneously for all derived schemes, functorialy splitting the HKR-filtration and rendering the circle action compatible with the de Rham differential, is, via Cartier duality, in a natural bijection with the set of filtered formal exponential maps $\widehat{{\mathbb{G}}_a}\to \widehat{{\mathbb{G}}_m}$. In particular, when the base $k$ is a field of characteristic zero, the set of choices is $k^{\ast }$.

8 pages, Typos fixed. To appear in Mathematical Research Letters