{"paper":{"title":"Locally finitely presented and coherent hearts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Carlos E. Parra, Manuel Saor\\'in, Simone Virili","submitted_at":"2019-08-01T22:44:29Z","abstract_excerpt":"Starting with a Grothendieck category $\\mathcal{G}$ and a torsion pair $\\mathbf{t}=(\\mathcal{T},\\mathcal{F})$ in $\\mathcal G$, we study the local finite presentability and local coherence of the heart $\\mathcal{H}_{\\mathbf{t}}$ of the associated Happel-Reiten-Smal{\\o} $t$-structure in the derived category $\\mathrm{Der} (\\mathcal{G})$. We start by showing that, in this general setting, the torsion pair $\\mathbf t$ is of finite type, if and only if it is quasi-cotilting, if and only if it is cosilting. We then proceed to study those $\\mathbf t$ for which $\\mathcal{H}_{\\mathbf{t}}$ is locally fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00649","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00649/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"}