{"paper":{"title":"Filtrations and Homological degrees of FI-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.RT","authors_text":"Liping Li, Nina Yu","submitted_at":"2015-11-10T02:57:40Z","abstract_excerpt":"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 an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02977","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}