The Koszul complex is the cotangent complex

Joan Millès (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We extend the Koszul duality theory of associative algebras to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent complex, involved in the cohomology theory of algebras over an operad, generalizes the Koszul complex.

Mots clés: Koszul duality; André-Quillen cohomologie; Cotangent complex

Domaines: K-théorie et homologie [math.KT]; Topologie algébrique [math.AT]

Joan Millès. The Koszul complex is the cotangent complex. International Mathematics Research Notices, 2012, 2012 (3), pp.607-650. ⟨10.1093/imrn/rnr034⟩. ⟨hal-00551945⟩