{"paper":{"title":"Local duality in algebra and topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.CT"],"primary_cat":"math.AT","authors_text":"Drew Heard, Gabriel Valenzuela, Tobias Barthel","submitted_at":"2015-11-11T15:05:02Z","abstract_excerpt":"The first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts. For any stable $\\infty$-category $\\mathcal{C}$ together with a collection of compact objects $\\mathcal{K} \\subset \\mathcal{C}$ we construct local cohomology and local homology functors satisfying an abstract version of local duality. When specialized to the derived category of a commutative ring $A$ and a suitable ideal in $A$, we recover the classical local duality due to Grothendieck as well as generalizations by Greenlees and May. More"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03526","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"}