Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.

Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

Rigidity of the frobenius, matlis reflexivity, and minimal flat resolutions

Douglas J Dailey, University of Nebraska - Lincoln

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.
http://digitalcommons.unl.edu/dissertations/AAI10099960

Share

COinS