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On simplicial commutative algebras with Noetherian homotopy | | James M Turner
; | | Date: |
9 Dec 2001 | | Subject: | Commutative Algebra; Algebraic Geometry; Algebraic Topology MSC-class: 13D03, 13D05, 18G30, 55S45, 55U99 | math.AC math.AG math.AT | | 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. | | Source: | arXiv, math.AC/0201063 | | Services: | Forum | Review | PDF | Favorites | |
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