Grothendieck Duality via Rigid Dualizing Complexes and Differential
Graded Algebras

    Amnon Yekutieli, Ben Gurion University, ISRAEL

Abstract:

In this talk I'll present a new approach to Grothendieck duality
on schemes. Our approach is based on Van den Bergh's idea of rigid
dualizing complexes.

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 case
of a scheme which is not flat over the base.

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