March 31, 2003

Amnon Yekutieli

Title: Grothendieck Duality via Rigid Dualizing Complexes and Differential Graded Algebras

Abstract:

In this talk I'll present a new approach to Grothendieck duality on schemes. Our approach is based on two main ideas: rigid dualizing complexes and perverse coherent sheaves.

We obtain most of the important features of Grothendieck duality, including explicit formulas, yet manage to avoid lengthy and difficult compatibility verifications. Our results apply to finite type schemes over a regular noetherian base ring, and hence are suitable for arithmetic geometry.

I will only discuss the algebraic part of the construction. The highlight of the talk will be the role of differential graded algebras in the arithemtic situation.

This is joint work with James Zhang (Univ. of Washington).