Connected simplicial algebras are Andr\'e-Quillen complete

Michael Donovan

Connected simplicial algebras are Andr\'e-Quillen complete

Algebraic Topology 2014-10-31 v1

Authors: Michael Donovan

Abstract

We modify a classical construction of Bousfield and Kan to define the Adams tower of a simplicial nonunital commutative algebra over a field k. We relate this construction to Radulescu-Banu's cosimplicial resolution, and prove that all connected simplicial algebras are complete with respect to Andr\'e-Quillen homology. This is a convergence result for the unstable Adams spectral sequence for commutative algebras over k.

Cite

@article{arxiv.1410.8244,
  title  = {Connected simplicial algebras are Andr\'e-Quillen complete},
  author = {Michael Donovan},
  journal= {arXiv preprint arXiv:1410.8244},
  year   = {2014}
}