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- W4285662882 abstract "This work concerns maps $varphi colon Rto S$ of commutative noetherian rings, locally of finite flat dimension. It is proved that the Andr'e-Quillen homology functors are rigid, namely, if $mathrm{D}_n(S/R;-)=0$ for some $nge 2$, then $mathrm{D}_n(S/R;-)=0$ for all $nge 2$ and $varphi$ is locally complete intersection. This extends Avramov's theorem that draws the same conclusion assuming $mathrm{D}_n(S/R;-)$ vanishes for all $ngg 0$, confirming a conjecture of Quillen. The rigidity of Andr'e-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 Andr'e-Quillen cohomology to Hochschild cohomology defined using the universal Atiyah class of $varphi$." @default.
- W4285662882 created "2022-07-17" @default.
- W4285662882 creator A5056968077 @default.
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- W4285662882 date "2020-10-25" @default.
- W4285662882 modified "2023-09-27" @default.
- W4285662882 title "Rigidity properties of the cotangent complex" @default.
- W4285662882 doi "https://doi.org/10.48550/arxiv.2010.13314" @default.
- W4285662882 hasPublicationYear "2020" @default.
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