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On Simplicial Commutative Algebras with Finite Andre-Quillen Homology | | James M Turner
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9 Jul 2003 | | Subject: | Commutative Algebra; Algebraic Topology MSC-class: 13D03; 55U35 | math.AC math.AT | | Abstract: | L. Avramov, following D. Quillen, posed a conjecture to the effect that if $R o A$ is a homomorphism of Noetherian rings then the André-Quillen homology on the category of A-modules satisfies: $D_{s}(A|R;-) = 0$ for $sgg 0$ implies $D_{s}(A|R;-) = 0$ for s>2. In an earlier paper, the author posed an extended version of this conjecture which considered A to be a simplicial commutative R-algebra with Noetherian homotopy such that the characteristic of $pi_{0}A$ is non-zero. In addition, a homotopy characterization of such algebras was described. The main goal of this paper is to develop a strategy for establishing this extended conjecture and provide a complete proof when R is Cohen-Macaulay of characteristic 2. | | Source: | arXiv, math.AC/0307113 | | Services: | Forum | Review | PDF | Favorites | |
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