On the degree-wise coherence of FJG-modules

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Abstract

In this work we study a kind of coherence condition on FJG-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 FJG-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 FJG-modules, introduced in Li-Ramos, 2016.

Original languageEnglish
Pages (from-to)873-895
Number of pages23
JournalNew York Journal of Mathematics
Volume23
StatePublished - 30 Jul 2017

Keywords

  • FJ-modules
  • Local cohomology
  • Representation stability

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