Nilpotency in the homotopy of simplicial commutative algebras

Details Nilpotency in the homotopy of simplicial commutative algebras Nilpotency in the homotopy of simplicial commutative algebras

2002-01-09

arxiv.org/abs/math/0201064v1

Mathematics

Commutative Algebra

17 pages

Scientific paper

In this paper, we study simplicial commutative algebras with finite Andr\'e-Quillen homology. Here we restrict our focus to simplicial algebras having characteristic 2. Our aim is to find a generalization of results established by the author. Our goal is to replace the finiteness condition on homotopy with a weaker condition expressed in terms of nilpotency for the action of the homotopy operations. Coupled with the finiteness assumption on Andr\'e-Quillen homology, this nilpotency condition provides a way to bound the height at which the homology vanishes. As a consequence, we establish a special case of an open conjecture of Quillen.

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