{"paper":{"title":"Projective spaces over $\\mathbb{F}_{1^{\\ell}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Koen Thas","submitted_at":"2016-07-15T14:03:38Z","abstract_excerpt":"In this essay we study various notions of projective space (and other schemes) over $\\mathbb{F}_{1^\\ell}$, with $\\mathbb{F}_1$ denoting the field with one element. Our leading motivation is the \"Hiden Points Principle,\" which shows a huge deviation between the set of rational points as closed points defined over $\\mathbb{F}_{1^\\ell}$, and the set of rational points defined as morphisms $\\texttt{Spec}(\\mathbb{F}_{1^\\ell}) \\mapsto \\mathcal{X}$. We also introduce, in the same vein as Kurokawa [13], schemes of $\\mathbb{F}_{1^\\ell}$-type, and consider their zeta functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04513","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"}