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Seminar

Fellowship of the Ring, National Seminar: How short can a module of finite projective dimension be? February 25, 2021 (01:30 PM PST - 03:00 PM PST)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Mark Walker (University of Nebraska)
Description

To attend this seminar, you must register in advance, by clicking HERE.

Video

How Short Can a Module of Finite Projective Dimension be-

Abstract/Media

To attend this seminar, you must register in advance, by clicking HERE.

Abstract: This is joint work with Srikanth Iyengar and Linquan Ma. I will discuss the question:



For a given Cohen-Macaulay local ring R, what is the minimum non-zero value of length(M), where M ranges over those R-modules having finite projective dimension?



In investigating this question, one is quickly led to conjecture that the answer is e(R), the Hilbert-Samuel multiplicity of R. It turns out that this can be established for rings having Ulrich modules, or, more generally, lim Ulrich sequences of modules, with certain properties. Moreover, there is a related conjecture concerning length(M) and the Betti numbers of M, and a conjecture concerning the Dutta multiplicity of M, which can also be established when certain Ulrich modules (or lim Ulrich sequences) exist.





**Due to a Zoom cloud glitch, there is some missing content in the beginning of the presentation.**

Asset no preview Notes 11.5 MB application/pdf

How Short Can a Module of Finite Projective Dimension be-