Let B/A be a pair of commutative rings. We propose a DG (differential graded) approach to the cotangent complex LB/A. Using a commutative semi-free DG ring resolution of B relative to A, we construct a complex of B-modules LCotB/A. This construction works more generally for a pair B/A of commutative DG rings. In the talk, we will explain all these concepts. Then we will discuss the important properties of the DG B-module LCotB/A. If time permits, we’ll outline some of the proofs. It is conjectured that for a pair of rings B/A, our LCotB/A coincides with the usual cotangent complex LB/A, which is constructed by simplicial methods. We shall also relate LCotB/A to modern homotopical versions of the cotangent complex.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
