On Simplicial Commutative Rings with Vanishing André-Quillen Homology

Details On Simplicial Commutative Rings with Vanishing André-Quillen Homology On Simplicial Commutative Rings with Vanishing André-Quillen Homology

1997-07-31

arxiv.org/abs/alg-geom/9707018v2

Mathematics

Commutative Algebra

14 pages, LaTeX2e

Scientific paper

We propose a generalization of a conjecture of D. Quillen, on the vanishing of Andr\'e-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.

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