{"paper":{"title":"Presheaves of triangulated categories and reconstruction of schemes","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Paul Balmer","submitted_at":"2001-11-05T17:04:05Z","abstract_excerpt":"To any triangulated category with tensor product $(K,\\otimes)$, we associate a topological space $Spc(K,\\otimes)$, by means of thick subcategories of $K$, a la Hopkins-Neeman-Thomason. Moreover, to each open subset $U$ of $Spc(K,\\otimes)$, we associate a triangulated category $K(U)$, producing what could be thought of as a presheaf of triangulated categories. Applying this to the derived category $(K,\\otimes):=(D^{perf}(X),\\otimes^L)$ of perfect complexes on a noetherian scheme $X$, the topological space $Spc(K,\\otimes)$ turns out to be the underlying topological space of $X$; moreover, for ea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111049","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"}