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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Oblatum 3-III-1999 & 3-V-2000¶Published online: 11 October 2000
Rights and permissions
About this article
Cite this article
Turner, J. On simplicial commutative algebras with vanishing André-Quillen homology. Invent. math. 142, 547–558 (2000). https://doi.org/10.1007/s002220000096
Published:
Issue Date:
DOI: https://doi.org/10.1007/s002220000096