Algebraic Geometry Working Seminar

Yunhai Xiang, Department of Pure Mathematics, University of Waterloo

"Introduction to derived categories"

Derived categories, developed by Verdier and Grothendieck in the 1960s, have been studied extensively by algebraic geometers. In particular a lot of algebraic geometers are interested in the derived category of coherent sheaves. For this talk, we will focus on the basics of derived categories (from a purely categorical standpoint). We begin by defining the homotopy category of complexes, and then we look at how to construct localizations of categories using roofs. Finally we define a derived category, show that it has a triangulated structure, and see how it could be used to interpret derived functors in a new light.

This seminar will be held jointly online and in person:

• Room: MC 5403
• Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438