论文标题
HKR同构的功能性
Functoriality of HKR isomorphisms
论文作者
论文摘要
对于平滑方案的封闭嵌入$ x \ hookrightArrow s $并进行固定的一阶分裂，可以在派生的方案$ x \ times^r_s x $和移位的正常捆绑$ \ m m i \ mathbb {n} _ {n} _ {x/s} [x/s} [x/s} [-1] $，arinkin的hkr同构和移动的正常捆绑$ \ m m i \ mathbb {n} _ {n} _ {n} Arinkin-căldăraru-Hablicsek和Grivaux。在本文中，我们研究了HKR同构的功能性属性，用于一系列封闭的嵌入$ x \ hookrightarrow y \ hookrightarrow s $。当我们称为低音Quillen类的特定同胞类别消失时，HKR同构起作用。我们还为HKR同构和低音Quillen类提供了理论解释。
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.
