New York Journal of Mathematics
Volume 23 (2017) 873-895


Eric Ramos

On the degree-wise coherence of FIG-modules

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Published: July 30, 2017
Keywords: FI-modules, representation stability, local cohomology
Subject: Primary: 18A25 , 05E10; secondary: 13D45, 16P70

In this work we study a kind of coherence condition on FIG-modules, which generalizes the usual notion of finite generation. We prove that a module is coherent, in the appropriate sense, if and only if its generators, as well as its torsion, appears in only finitely many degrees. Using this technical result, we prove that the category of coherent FIG-modules is abelian, independent of any assumptions on the group G, or the coefficient ring k. Following this, we consider applications towards the local cohomology theory of FIG-modules, introduced in Li-Ramos, 2016.


The author was supported by NSF grant DMS-1502553.

Author information

Department of Mathematics, University of Wisconsin - Madison.