论文标题
Cotangent复合物的刚性特性
Rigidity properties of the cotangent complex
论文作者
论文摘要
这项工作涉及$φ\ colon r \ to s $ sumportive noetherian戒指的s $，该环的本地扁平尺寸。事实证明，André-Quillen同源性函数是刚性的，也就是说，如果$ \ mathrm {d} _n（s/r; - ）= 0 $，对于某些$ n \ ge 2 $，则$ \ m mathrm {d} _n（s/r; - ）= 0 $ n $ n \ ge 2 $ $ $ $ $ $ $ uctection cute cutters cutters cutte cutters cutte cutters cutte cutter。这扩展了Avramov的定理，假设$ \ mathrm {d} _n（s/r; - ）$ nishes $ nishes nishes nishes nishes nishes nishes nishes nishes nishes nishes nishes to the ventumens的定理。 André-Quillen函子的刚性是从更一般的结果中推论出的，该结果回答了Avramov和Herzog提出的一个问题，并构成了Vasconcelos的猜想，这是第一作者最近证明的。导致这些结果的新见解涉及从安德烈·奎伦（André-Quillen）共同学到霍奇希尔德（Hochschild）共同体的地图，使用$φ$的通用atiyah类定义。
This work concerns maps $φ\colon R\to S$ of commutative noetherian rings, locally of finite flat dimension. It is proved that the André-Quillen homology functors are rigid, namely, if $\mathrm{D}_n(S/R;-)=0$ for some $n\ge 2$, then $\mathrm{D}_n(S/R;-)=0$ for all $n\ge 2$ and $φ$ is locally complete intersection. This extends Avramov's theorem that draws the same conclusion assuming $\mathrm{D}_n(S/R;-)$ vanishes for all $n\gg 0$, confirming a conjecture of Quillen. The rigidity of André-Quillen functors is deduced from a more general result about the higher cotangent modules which answers a question raised by Avramov and Herzog, and subsumes a conjecture of Vasconcelos that was proved recently by the first author. The new insight leading to these results concerns the equivariance of a map from André-Quillen cohomology to Hochschild cohomology defined using the universal Atiyah class of $φ$.
