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SUMMARY:Mark Walker (University of Nebraska)
DTSTART:20210225T213000Z
DTEND:20210225T230000Z
DTSTAMP:20260423T021437Z
UID:FOTR/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/40/">Ho
 w short can a module of finite projective dimension be?</a>\nby Mark Walke
 r (University of Nebraska) as part of Fellowship of the Ring\n\n\nAbstract
 \nThis is joint work with Srikanth Iyengar and Linquan Ma. I will discuss 
 the question:\n\nFor a given Cohen-Macaulay local ring R\, what is the min
 imum non-zero value of length(M)\, where M ranges over those R-modules hav
 ing finite projective dimension?\n\nIn investigating this question\, one i
 s quickly led to conjecture that the answer is e(R)\, the Hilbert-Samuel m
 ultiplicity of R. It turns out that this can be established for rings havi
 ng Ulrich modules\, or\, more generally\, lim Ulrich sequences of modules\
 , with certain properties. Moreover\, there is a related conjecture concer
 ning length(M) and the Betti numbers of M\, and a conjecture concerning th
 e Dutta multiplicity of M\, which can also be established when certain Ulr
 ich modules (or lim Ulrich sequences) exist.\n
LOCATION:https://researchseminars.org/talk/FOTR/40/
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