{"paper":{"title":"Characterizing Serre quotients with no section functor and applications to coherent sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Markus Lange-Hegermann, Mohamed Barakat","submitted_at":"2012-10-04T12:55:15Z","abstract_excerpt":"We prove an analogon of the the fundamental homomorphism theorem for certain classes of exact and essentially surjective functors of Abelian categories $\\mathscr{Q}:\\mathcal{A} \\to \\mathcal{B}$. It states that $\\mathscr{Q}$ is up to equivalence the Serre quotient $\\mathcal{A} \\to \\mathcal{A} / \\mathrm{ker} \\mathscr{Q}$, even in cases when the latter does not admit a section functor. For several classes of schemes $X$, including projective and toric varieties, this characterization applies to the sheafification functor from a certain category $\\mathcal{A}$ of finitely presented graded modules t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1425","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"}