Title:
Rigidity, Residues and Duality: Overview and Recent Progress

Speaker:
Amnon Yekutieli, BGU

Abstract:
In this lecture we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results.

Unlike all previous approaches to Grothendieck Duality, the rigid approach concentrates on the construction of rigid residue complexes over rings, and their intricate yet robust properties. Most of the lecture will about the results for rings.

The geometrization, i.e. the passage to rigid residue complexes on schemes and Deligne-Mumford (DM) stacks, by gluing, is fairly easy. In the geometric part of the theory, the main results are the Rigid Residue Theorem and the Rigid Duality Theorem for proper maps between schemes, and for tame proper maps between DM stacks. These results will only be outlined briefly.

More details are available in the eprint with the same title at
https://arxiv.org/abs/2102.00255

The lecture notes are be available at
http://www.math.bgu.ac.il/~amyekut/lectures/RRD-2021/notes.pdf

and the slides are here
http://www.math.bgu.ac.il/~amyekut/lectures/RRD-2021/slides.pdf

(updated 20 May 2021)