2002/10/02 by Luchézar L. Avramov, L. L. Avramov, Srikanth B. Iyengar +3 · 1 citation
Mathematics · #13D03 #13H10 #14B25 (Primary) #14M10 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AC #math.KT #msc:13D03 #msc:13H10 #msc:14B25 #msc:14M10
paper · pdf · doi:10.48550/arxiv.math/0210037
30 pages. To be published in Ann. Sci. Ecole Norm. Sup. (4)
arxiv created 2002/10/02 · openalex publication_date 2002/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a homomorphism of commutative noetherian rings ϕ: R → S, Daniel Quillen conjectured in 1970 that if the Andre-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 ϕ∘ψ=\idS. 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→ R→ S for which the S-algebra TorR(S,S) is finitely generated.