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Rigidity Of The Frobenius, Matlis Reflexivity, And Minimal Flat Resolutions, Douglas J. Dailey

Department of Mathematics: Dissertations, Theses, and Student Research

Let R be a commutative, Noetherian ring of characteristic p >0. Denote by f the Frobenius endomorphism, and let R^(e) denote the ring R viewed as an R-module via f^e. 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 Tor_i^R(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 …