Document Type
Article
Publication Title
Inventiones Mathematicae
Abstract
In this paper, we study the André-Quillen homology of simplicial commutative ℓ-algebras, ℓ a field, having certain vanishing properties. When ℓ 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, having non-zero characteristic.
First Page
547
Last Page
558
DOI
10.1007/s002220000096
Publication Date
1-1-2000
Recommended Citation
Turner, James M., "On simplicial commutative algebras with vanishing André-Quillen homology" (2000). University Faculty Publications and Creative Works. 542.
https://digitalcommons.calvin.edu/calvin_facultypubs/542