Andre-Quillen homology of algebra retracts
| dc.creator | Avramov, L. L. | |
| dc.creator | Iyengar, S. | |
| dc.date | 2002-10-02 | |
| dc.date.accessioned | 2026-07-07T04:51:28Z | |
| dc.date.available | 2026-07-07T04:51:28Z | |
| dc.description | Given a homomorphism of commutative noetherian rings $ϕ: R \to S$, Daniel Quillen conjectured in 1970 that if the Andre-Quillen homology functors $D_n(S|R,-)$ vanish for all $n \gg 0$, then they vanish for all $n \ge 3$. We prove the conjecture under the additional hypothesis that there exists a homomorphism of rings $ψ: S \to R$ such that $ϕ\circψ=\id_S$. More precisely, in this case we show that $ψ$ is complete intersection at $ϕ^{-1}(\fn)$ for every prime ideal $\fn$ of $S$. Using these results, we describe all algebra retracts $S\to R\to S$ for which the $S$-algebra $Tor^R(S,S)$ is finitely generated. | |
| dc.description | 30 pages. To be published in Ann. Sci. Ecole Norm. Sup. (4) | |
| dc.identifier | https://arxiv.org/abs/math/0210037 | |
| dc.identifier | http://arxiv.org/abs/math/0210037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65155 | |
| dc.subject | Commutative Algebra | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 13D03; 14B25 (Primary), 13H10; 14M10 (Secondary) | |
| dc.title | Andre-Quillen homology of algebra retracts | |
| dc.type | text |