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arXiv · 2002.00017

Functoriality of HKR isomorphisms

Shengyuan Huang
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Abstract

For a closed embedding of smooth schemes $X\hookrightarrow S$ with a fixed first order splitting, one can construct HKR isomorphisms between the derived scheme $X\times^R_S X$ and the total space of the shifted normal bundle $\mathbb{N}_{X/S}[-1]$, due to Arinkin-C\u{a}ld\u{a}raru, Arinkin-C\u{a}ld\u{a}raru-Hablicsek, and Grivaux. In this paper, we study functoriality property of the HKR isomorphisms for a sequence of closed embeddings $X\hookrightarrow Y\hookrightarrow S$. The HKR isomorphism is functorial when a certain cohomology class, which we call the Bass-Quillen class, vanishes. We obtain Lie theoretic interpretations for the HKR isomorphisms and for the Bass-Quillen class as well.

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Shengyuan Huang. 2020-01-31. Functoriality of HKR isomorphisms. https://arxiv.org/abs/2002.00017

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