An Introduction to Derived Categories in Geometry (Parts 1-3)
University of Wisconsin, U.S.A.
(Part 1) The theory of derived categories was first developed in the sixties by Grothendieck and Verdier to deal with questions of duality in algebraic geometry. Since then, this theory has found important applications in geometry, representation theory and mathematical physics. Our goal here is to present an introduction to some aspects of derived categories as they relate to algebraic geometry and to briefly discuss some key recent developments. The first talk will cover definitions and first properties, with the focus being on examples. We hope to conclude with the Beilinon spectral sequence and a discussion of tilting.