Ben-Gurion University
	Algebraic Geometry and Number Theory Seminar
Title: Residues and Duality for Schemes and Stacks
Speaker: Amnon Yekutieli
(Ben-Gurion University)
Date: Wednesday; December 19, 2012
Time: 15:00-16:30
Place: Room -101
Let K be a regular noetherian commutative ring. I consider finite type
commutative K-algebras and K-schemes. I will begin by explaining the
theory of rigid residue complexes on K-algebras, that was developed by
J. Zhang and myself several years ago. Then I will talk about the
geometrization of this theory: rigid residue complexes on K-schemes and
their functorial properties. For any map between K-schemes there is a
rigid trace homomorphism (that usually does not commute with the
differentials). When the map of schemes is proper, the rigid trace does
commute with the differentials (this is the Residue Theorem), and it
induces Grothendieck Duality. Then I will move to finite type
Deligne-Mumford K-stacks. Any such stack has a rigid residue complex on
it, and for any map between stacks there is a trace homomorphism. These
facts are rather easy consequences of the corresponding facts for
schemes, together with etale descent. I will finish by presenting two
conjectures, that refer to Grothendieck Duality for proper maps between
DM stacks. A key condition here is that of tame map of stacks.
Technion Math Net-2 (TECHMATH2)
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