{"paper":{"title":"Localizing and colocalizing subcategories on schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Ana Jerem\\'ias, Eduardo Loureiro, Leovigildo Alonso","submitted_at":"2024-05-16T18:23:51Z","abstract_excerpt":"A full triangulated subcategory $\\mathsf{L} \\subset \\mathsf{T}$ of triangulated category $\\mathsf{T}$ is localizing if it is stable for coproducts. If, further, $\\mathsf{T}$ is $\\otimes$-triangulated, we say that $\\mathsf{H}$ is $\\otimes$-ideal if $F \\otimes G \\in \\mathsf{L}$ for all $G \\in \\mathsf{L}$ and all $F \\in \\mathsf{T}$. Analogously, a full triangulated subcategory $\\mathsf{C} \\subset \\mathsf{T}$ is colocalizing if it is stable for products. If, further, $\\mathsf{T}$ is closed, i.e. $\\otimes$-triangulated with internal homs (denoted $[-,-]$), we say that $\\mathsf{C}$ is $\\mathcal{H}$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.10383","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/2405.10383/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"}