{"paper":{"title":"Cech Cohomology of Semiring Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jaiung Jun","submitted_at":"2015-03-04T17:09:10Z","abstract_excerpt":"A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \\v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\\mathbb{P}^n_M$, a projective space over a totally ordered idempotent semifield $M$, we show that \\v{C}ech cohomology theory is in agreement with the classical computation. Finally, we classify all invertible sheaves on $X=\\mathbb{P}^n_M$ by computing the Picard group of $X$ explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01389","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"}