Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Filtrations and Homological degrees of FI-modules   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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The categories of this paper are: stat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys