{"paper":{"title":"Higher $K$-Groups of Smooth Projective Curves Over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hourong Qin, Qingzhong Ji","submitted_at":"2011-12-27T04:24:22Z","abstract_excerpt":"Let $X$ be a smooth projective curve over a finite field $\\mathbb{F}$ with $q$ elements. For $m\\geq 1,$ let $X_m$ be the curve $X$ over the finite field $\\mathbb{F}_m$, the $m$-th extension of $\\mathbb{F}.$ Let $K_n(m)$ be the $K$-group $K_n(X_m)$ of the smooth projective curve $X_m.$\n  In this paper, we study the structure of the groups $K_n(m).$ If $l$ is a prime, we establish an analogue of Iwasawa theorem in algebraic number theory for the orders of the $l$-primary part $K_n(l^m)\\{l\\}$ of $K_n(l^m)$. In particular, when $X$ is an elliptic curve $E$ defined over $\\mathbb{F},$ our method det"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5920","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"}