{"paper":{"title":"Geometry of the arithmetic site","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alain Connes, Caterina Consani","submitted_at":"2015-02-19T14:21:40Z","abstract_excerpt":"We introduce the Arithmetic Site: an algebraic geometric space deeply related to the non-commutative geometric approach to the Riemann Hypothesis. We prove that the non-commutative space quotient of the adele class space of the field of rational numbers by the maximal compact subgroup of the idele class group, which we had previously shown to yield the correct counting function to obtain the complete Riemann zeta function as Hasse-Weil zeta function, is the set of geometric points of the arithmetic site over the semifield of tropical real numbers. The action of the multiplicative group of posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05580","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"}