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arXiv · 1303.2937

Periodic modules over Gorenstein local rings

Amanda Croll
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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}]-module associated to R. This module, denoted J(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.

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Amanda Croll. 2013-04-26. Periodic modules over Gorenstein local rings. https://arxiv.org/abs/1303.2937

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