Simplicial commutative algebras with vanishing Andre-Quillen homology

Details Simplicial commutative algebras with vanishing Andre-Quillen homology Simplicial commutative algebras with vanishing Andre-Quillen homology

2002-01-09

arxiv.org/abs/math/0201065v1

Inventiones mathematicae 142 (3) (2000), pp. 547-558

Mathematics

Commutative Algebra

11 pages

Scientific paper

In this paper, we study the Andr\'e-Quillen homology of simplicial commutative $\ell$-algebras, $\ell$ a field, having certain vanishing properties. When $\ell$ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for algebras of finite type over Noetherian rings, which have non-zero characteristic.

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