{"paper":{"title":"The local symbol complex of a Reciprocity Functor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Evangelia Gazaki","submitted_at":"2015-04-30T15:40:58Z","abstract_excerpt":"For a reciprocity functor $\\mathcal{M}$ we consider the local symbol complex $\\mathcal{M}\\otimes^{M}\\mathbb{G}_{m}(\\eta_{C})\\to\\oplus_{P\\in C}\\mathcal{M}(k)\\to\\mathcal{M}(k)$, where $C$ is a smooth complete curve over an algebraically closed field $k$ with generic point $\\eta_{C}$ and $\\otimes^{M}$ is the product of Mackey functors. We prove that if $\\mathcal{M}$ satisfies certain conditions, then the homology of the above complex is isomorphic to the $K$-group of reciprocity functors $T(\\mathcal{M},\\underline{CH}_{0}(C)^{0})(Spec k)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08277","kind":"arxiv","version":2},"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"}