Frobenius Betti numbers of finite length modules

Abstract: Let $(R, m)$ be a Noetherian local ring of dimension $d > 0$ and $M$ be a finitely generated $R$-module of finite length. Suppose char R = $p > 0$ and $d = 1.$ De Stefani, Huneke and Núñez-Betancourt explored the question: what vanishing conditions on the Frobenius Betti numbers force projective dimension of $M$ to be finite. In this talk we will discuss the question for $d ≥ 1.$ This is joint work with Ian Aberbach.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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