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Choices of HKR isomorphisms
Published 9 Oct 2023 in math.AG, math.KT, math.NT, and math.QA | (2310.05859v2)
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 $k\ast$.
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