{"paper":{"title":"Weight structures vs. $t$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.KT","authors_text":"M.V. Bondarko","submitted_at":"2007-04-30T19:53:00Z","abstract_excerpt":"This paper is dedicated to triangulated categories endowed with weight structures (a new notion; D. Pauksztello has independently introduced them as co-t-structures). This axiomatizes the properties of stupid truncations of complexes in $K(B)$. We also construct weight structures for Voevodsky's categories of motives and for various categories of spectra. A weight structure $w$ defines Postnikov towers of objects; these towers are canonical and functorial 'up to morphisms that are zero on cohomology'. For $Hw$ being the heart of $w$ (in $DM_{gm}$ we have $Hw=Chow$) we define a canonical conser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.4003","kind":"arxiv","version":9},"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"}