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arXiv · 2310.05859

Choices of HKR isomorphisms

Marco Robalo
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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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Marco Robalo. 2023-10-09. Choices of HKR isomorphisms. https://arxiv.org/abs/2310.05859

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