{"paper":{"title":"Cech cohomology over $\\mathbb{F}_{1^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaret Flores, Matt Szczesny, Oliver Lorscheid","submitted_at":"2015-11-21T12:32:37Z","abstract_excerpt":"In this text, we generalize Cech cohomology to sheaves $\\mathcal F$ with values in blue $B$-modules where $B$ is a blueprint with $-1$. If $X$ is an object of the underlying site, then the cohomology sets $H^l(X,\\mathcal F)$ turn out to be blue $B$-modules. For locally free $\\mathcal O_X$-module $\\mathcal F$ on a monoidal scheme $X$, we prove that $H^l(X,\\mathcal F)^+=H^l(X^+,\\mathcal F^+)$ where $X^+$ is the scheme associated with $X$ and $\\mathcal F^+$ is the locally free $\\mathcal O_{X^+}$-module associated with $\\mathcal F$.\n  In an appendix, we show that the naive generalization of cohomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06875","kind":"arxiv","version":1},"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"}