Title: On simplicial commutative algebras with Noetherian homotopy
Authors: James M Turner
Address: Calvin College
E-mail: jturner@calvin.edu
ArXiv id. no.: math.AT/0201063
MSC-class: 13D03, 13D05, 18G30, 55S45, 55U99
Abstract: In this paper, a strategy is developed studying a simplicial
commutative algebra A whose zeroth homotopy group is a Noetherian ring B
and whose higher homotopy groups are finite over B. The strategy replaces A
with a connected simplicial supplemented k(q)-algebra, for each prime ideal q
in B, which preserves much of the Andre-Quillen homology of A. The methods
for this construction involves a mixture of methods of homotopy theory
(e.g. Postnikov towers) with methods of commutative algebras (e.g. completions,
Cohen factorizations). We finish by indicating how these methods resolve a
more general form of a conjecture posed by Quillen.