Filtrations and Homological degrees of FI-modules

Liping Li Nina Yu

K-Theory and Homology Representation Theory Rings and Algebras mathscidoc:1702.02010

J. Algebra, 472, 369-398, 2017
Let k be a commutative Noetherian ring. In this paper we consider filtered modules of the category FI firstly introduced by Nagpal. We show that a finitely generated FI-module V is filtered if and only if its higher homologies all vanish, and if and only if a certain homology vanishes. Using this homological characterization, we characterize finitely generated FI-modules V whose projective dimension is finite, and describe an upper bound for it. Furthermore, we give a new proof for the fact that V induces a finite complex of filtered modules, and use it as well as a result of Church and Ellenberg to obtain another upper bound for homological degrees of V.
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  title={Filtrations and Homological degrees of FI-modules},
  author={Liping Li, and Nina Yu},
  booktitle={J. Algebra},
Liping Li, and Nina Yu. Filtrations and Homological degrees of FI-modules. 2017. Vol. 472. In J. Algebra. pp.369-398.
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