1997/07/31 by James M. Turner, Turner, James M.
Mathematics · #18G20 #18G30 #18G55 #55S45 #55T10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 13D03 #Quantum Algebra (math.QA) #Secondary: 13D40
paper · pdf · doi:10.48550/arxiv.alg-geom/9707018
openalex publication_date 1997/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a generalization of a conjecture of D. Quillen, on the vanishing of André-Quillen homology, to simplicial commutative rings. This conjecture characterizes a notion of local complete intersection, extended to the simplicial setting, under a suitable hypothesis on the local characteristic. Further, under the condition of finite-type homology, we then prove the conjecture in the case of a simplicial commutative algebra augmented over a field of non-zero characteristic. As a consequence, we obtain a proof of Quillen's conjecture for a Noetherian commutative algebra - again augmented over a field of non-zero characteristic.