Andre-Quillen homology of commutative algebras

Details Andre-Quillen homology of commutative algebras Andre-Quillen homology of commutative algebras

2006-09-05

arxiv.org/abs/math/0609151v1

Mathematics

Commutative Algebra

32 pages; to appear in: Interactions between homotopy theory and algebra (Chicago 2004), Contemp. Math

Scientific paper

These notes are an introduction to basic properties of Andre-Quillen homology for commutative algebras. They are an expanded version of my lectures at the summer school: Interactions between homotopy theory and algebra, University of Chicago, 26th July - 6th August, 2004. The aim is to give fairly complete proofs of characterizations of smooth homomorphisms and of locally complete intersection homomorphisms in terms of vanishing of Andre-Quillen homology. The choice of the material, and the point of view, are guided by these goals.

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