TY - JOUR
T1 - On the degree-wise coherence of FJG-modules
AU - Ramos, Eric
N1 - Publisher Copyright:
© 2017, University at Albany. All rights reserved.
PY - 2017/7/30
Y1 - 2017/7/30
N2 - 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.
AB - 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.
KW - FJ-modules
KW - Local cohomology
KW - Representation stability
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M3 - Article
AN - SCOPUS:85026734722
VL - 23
SP - 873
EP - 895
JO - New York Journal of Mathematics
JF - New York Journal of Mathematics
ER -