2020
DOI: 10.1090/proc/14989
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Frobenius Betti numbers and syzygies of finite length modules

Abstract: Let (R, m) be a local (Noetherian) ring of dimension d and M a finite length R-module with free resolution G•. De Stefani, Huneke, and Núñez-Betancourt explored two questions about the properties of resolutions of M . First, in characteristic p > 0, what vanishing conditions on the Frobenius Betti numbers, β F i (M, R) := lime→∞ λ(F e (G•))/p ed , force pd R M < ∞. Second, if pd R M = ∞, does this force d + 2nd or higher syzygies of M to have infinite length.For the first question, they showed, under rather re… Show more

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