{"paper":{"title":"Moduli Operad over F1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matilde Marcolli, Yuri I. Manin","submitted_at":"2013-02-26T18:38:41Z","abstract_excerpt":"In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad $\\{\\bar{M}_{0,n+1}\\}$ can be endowed with natural descent data that allow it to be considered as the lift to ${\\rm Spec}\\,\\Z$ of an operad over $\\F_1$. The relevant descent data are based on a notion of constructible sets and constructible functions over $\\F_1$, which describes suitable differences of torifications with a positivity condition on the class in the Grothendieck ring. More generally, we do the same for the operads $\\{T_{d,n+1}\\}$ (whose components were) introduced in [5]. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6526","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"}