Periodic modules over Gorenstein local rings

Authors

Amanda Croll, University of Nebraska-LincolnFollow

Date of this Version

Spring 4-12-2013

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Srikanth Iyengar. Lincoln, Nebraska: May, 2013

Copyright (c) 2013 Amanda Croll

Abstract

It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t,t^{-1}] associated to R. This module, denoted (R), is the free Z[t,t^{-1}]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The main result is a structure theorem for J(R) when R is a complete Gorenstein local ring; the link between periodicity and torsion stated above is a corollary.

Advisor: Srikanth Iyengar