{"paper":{"title":"Hearts of t-structures in the derived category of a commutative Noetherian ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Carlos E. Parra, Manuel Saor\\'in","submitted_at":"2014-09-22T17:25:17Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring and let $\\mathcal D(R)$ be its (unbounded) derived category. We show that all compactly generated t-structures in $\\mathcal D(R)$ associated to a left bounded filtration by supports of Spec$(R)$ have a heart which is a Grothendieck category. Moreover, we identify all compactly generated t-structures in $\\mathcal D(R)$ whose heart is a module category. As geometric consequences for a compactly generated t-structure $(\\mathcal{U},\\mathcal{U}^\\perp [1])$ in the derived category $\\mathcal{D}(\\mathbb{X})$ of a Noetherian scheme $\\mathbb{X}$, we get the follo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6254","kind":"arxiv","version":2},"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"}