HKR同构的功能性

摘要：

对于具有固定一阶分裂的光滑概形$X\hookrightarrow S$的闭嵌入，由于Arinkin-Czynldraru-Hablicsek和Grivaux，我们可以构造导出格式$X\times^R_S X$和移位法丛$\mathbb{N}_{X/S}[-1]$的全空间之间的HKR同构.本文研究了闭嵌入序列$X\hookrightarrow Y\hookrightarrow S$的HKR同构的函性.当一个特定的上同调类，我们称之为Bass-Quillen类，消失时，HKR同构是函子的。我们得到的HKR同构和Bass-Quillen类的李群理论解释。

英文摘要：

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-Căldăraru, Arinkin-Căldăraru-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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