Home /  Workshop /  Schedules /  Castelnuovo-Mumford Regularity for Standard Graded Rings Over Noetherian Base Rings

Castelnuovo-Mumford Regularity for Standard Graded Rings Over Noetherian Base Rings

Introductory Workshop: Commutative Algebra January 22, 2024 - January 26, 2024

January 25, 2024 (10:00 AM PST - 11:00 AM PST)
Speaker(s): Aldo Conca (Università di Genova)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Castelnuovo-Mumford Regularity for Standard Graded Rings Over Noetherian Base Rings Part 3

Abstract

We will present a self-contained introduction to the Castelnuovo–Mumford regularity for standard graded rings over general Noetherian base rings. In particular, we will show that it can be defined in terms of the vanishing of local cohomology modules, vanishing of Koszul homology and the shifts in a minimal free resolution. We will present a proof of a classical result on regularity of the powers of an ideal due originally to Cutkosky, Herzog and Trung and, independently, to Kodiyalam. Variants for products of powers and generalizations will be discussed as well. Examples of determinantal or combinatorial nature will be presented.

Supplements No Notes/Supplements Uploaded
Video/Audio Files

Castelnuovo-Mumford Regularity for Standard Graded Rings Over Noetherian Base Rings Part 3

Troubles with video?

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.