André-Quillen homology of algebra retracts |
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Authors: | Luchezar L Avramov |
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Institution: | Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA Current address: Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA; Pure Mathematics, Hicks Building, University of Sheffield, Sheffield S3 7RH, UK Current address: Department of Mathematics, University of Missouri, Columbia, MO 65201, USA |
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Abstract: | Given a homomorphism of commutative noetherian rings ?:R→S, Daniel Quillen conjectured in 1970 that if the André-Quillen homology functors Dn(S∣R;−) vanish for all n?0, then they vanish for all n?3. We prove the conjecture under the additional hypothesis that there exists a homomorphism of rings ψ:S→R such that ?°ψ=idS. More precisely, in this case we show that ψ is a complete intersection at for every prime ideal of S. Using these results, we describe all algebra retracts S→R→S for which the algebra Tor•R(S,S) is finitely generated over Tor0R(S,S)=S. |
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