|Date: Friday, February 23, 2018
Location: 1360 East Hall (12:10 PM to 2:00 PM)
Title: The Cotangent Complex and the Derived Philosophy
Abstract: In this talk, we will introduce a derived variant of the module of Kahler differentials, which goes by the name of the Cotangent Complex. When studying deformation theory, classical algebraic geometry only provides us with tools to study deformations of smooth schemes; however, the cotangent complex allows us to extend these results to the non-smooth case. This is achieved following the derived philosophy: approximating poorly behaved rings with good ones in the same way that in homological algebra we approximate modules by taking free resolutions.
The underlying goal of this talk is to introduce the audience to different ideas underlying derived algebraic geometry while avoiding the technically charged language found in the literature. We will try to keep the talk accessible by focusing our energy in analogies with homological algebra, and avoiding the formalism of model categories introduced by Quillen.
Speaker: Attilio Castano
Institution: University of Michigan