Séminaires : Séminaire d'Algèbre

Let B/AB/A be a pair of commutative rings. We propose an algebraic approach to the cotangent complex LB/ALB/A​. Using commutative semi-free DG ring resolutions of B relative to A, we construct a complex of BB-modules LCotB/ALCotB/A​. This construction works more generally for a pair B/AB/A of commutative DG rings.In the talk, we will explain all these concepts. Then we will discuss the important properties of the DG BB-module LCotB/ALCotB/A​. It time permits, we'll outline some of the proofs.It is conjectured that for a pair of rings B/AB/A, our LCotB/ALCotB/A​ coincides with the usual cotangent complex LB/ALB/A​, which is constructed by simplicial methods. We shall also relate LCotB/ALCotB/A​ to modern homotopical versions of the cotangent complex.