{"paper":{"title":"Sequences of ICE-closed subcategories via preordered $\\tau^{-1}$-rigid modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eric J. Hanson","submitted_at":"2024-10-02T19:10:47Z","abstract_excerpt":"Let $\\Lambda$ be a finite-dimensional basic algebra. Sakai recently used certain sequences of image-cokernel-extension-closed (ICE-closed) subcategories of finitely generated $\\Lambda$-modules to classify certain (generalized) intermediate $t$-structures in the bounded derived category. We classifying these \"contravariantly finite ICE-sequences\" using concepts from $\\tau$-tilting theory. More precisely, we introduce \"cogen-preordered $\\tau^{-1}$-rigid modules\" as a generalization of (the dual of) the \"TF-ordered $\\tau$-rigid modules\" of Mendoza and Treffinger. We then establish a bijection bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.01963","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.01963/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}