Analytic Hochschild-Kostant-Rosenberg Theorem

Jack Kelly; Kobi Kremnizer; Devarshi Mukherjee

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arXiv · 2111.03502

Analytic Hochschild-Kostant-Rosenberg Theorem

Jack Kelly·Kobi Kremnizer·Devarshi Mukherjee

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Abstract

Let $R$ be a Banach ring. We prove that the category of chain complexes of complete bornological $R$-modules (and several related categories) is a derived algebraic context in the sense of Raksit. We then use the framework of derived algebra to prove a version of the Hochschild-Kostant-Rosenberg Theorem, which relates the circle action on the Hochschild algebra to the de Rham-differential-enriched-de Rham algebra of a simplicial, commutative, complete bornological algebra. This has a geometric interpretation in the language of derived analytic geometry, namely, the derived loop stack of a derived analytic stack is equivalent to the shifted tangent stack. Using this geometric interpretation we extend our results to derived schemes.

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BibTeX RIS

Jack Kelly, Kobi Kremnizer, Devarshi Mukherjee. 2021-11-05. Analytic Hochschild-Kostant-Rosenberg Theorem. https://arxiv.org/abs/2111.03502

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