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Rigidity of the frobenius, matlis reflexivity, and minimal flat resolutions
Abstract
Let R be a commutative, Noetherian ring of characteristic p > 0. Denote by f R → R the Frobenius endomorphism, and let R(e) denote the ring R viewed as an R-module via fe. Following on classical results of Peskine, Szpiro, and Herzog, Marley and Webb use flat, cotorsion module theory to show that if R has finite Krull dimension, then an R-module M has finite flat dimension if and only if ToriR(R (e),M) = 0 for all i > 0 and infinitely many e > 0. Using methods involving the derived category, we show that one only needs vanishing for dim R +1 consecutive values of i and infinitely many values of e to conclude that M has finite flat dimension. We also study a general notion of Matlis duality and give a change of rings result for Matlis reflexive modules.
Subject Area
Mathematics
Recommended Citation
Dailey, Douglas J, "Rigidity of the frobenius, matlis reflexivity, and minimal flat resolutions" (2016). ETD collection for University of Nebraska-Lincoln. AAI10099960.
https://digitalcommons.unl.edu/dissertations/AAI10099960