{"paper":{"title":"Local Picard Group of Binoids and Their Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Davide Alberelli","submitted_at":"2016-11-06T14:51:55Z","abstract_excerpt":"We begin by introducing schemes of binoids, invertible $\\mathcal{O}_M$-sets and cohomology of sheaves of abelian groups defined on schemes of binoids. We define the so-called punctured combinatorial \\v{C}ech-Picard complex, whose first cohomology computes $\\mathrm{Pic}^{\\mathrm{loc}}(M)$, the local Picard group of a binoid. We look then at simplicial binoids, whose spectrum presents very nice combinatorial properties. We prove that the cohomology of a constant sheaf on this punctutured spectra can be computed entirely in terms of simplicial cohomology. Through some other results, we prove that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01788","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"}