How short can a module of finite projective dimension be?

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.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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