{"paper":{"title":"Graphs, $\\mathbb{F}_1$-schemes and virtual mixed Tate motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Koen Thas, Manuel Merida-Angulo","submitted_at":"2016-11-23T14:19:14Z","abstract_excerpt":"In a number of recent works [6, 7] the authors have introduced and studied a functor $\\mathcal{F}_k$ which associates to each loose graph $\\Gamma$ -which is similar to a graph, but where edges with $0$ or $1$ vertex are allowed - a $k$-scheme, such that $\\mathcal{F}_k(\\Gamma)$ is largely controlled by the combinatorics of $\\Gamma$. Here, $k$ is a field, and we allow $k$ to be $\\mathbb{F}_1$, the field with one element. For each finite prime field $\\mathbb{F}_p$, it is noted in [6] that any $\\mathcal{F}_k(\\Gamma)$ is polynomial-count, and the polynomial is independent of the choice of the field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07806","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"}