2002/01/08 by James M Turner, Turner, James M
Mathematics · #13D03 #13D05 #18G30 #55S45 #55U99 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #math.AT #msc:13D03 #msc:13D05 #msc:18G30 #msc:55S45 #msc:55U99
paper · pdf · doi:10.48550/arxiv.math/0201063
10 pages
arxiv created 2002/01/08 · arxiv updated 2009/11/30
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.