{"paper":{"title":"Large $3$-groups of automorphisms of algebraic curves in characteristic $3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2013-12-18T12:16:08Z","abstract_excerpt":"Let $S$ be a $p$-subgroup of the $\\K$-automorphism group $\\aut(\\cX)$ of an algebraic curve $\\cX$ of genus $\\gg\\ge 2$ and $p$-rank $\\gamma$ defined over an algebraically closed field $\\mathbb{K}$ of characteristic $p\\geq 3$.In this paper we prove that if $|S|>2(\\gg-1)$ then one of the following cases occurs. \\begin{itemize} \\item[(i)] $\\gamma=0$ and the extension $\\K(\\cX)/\\K(\\cX)^S$ completely ramifies at a unique place, and does not ramify elsewhere. \\item[(ii)] $\\gamma>0$, $p=3$, $\\cX$ is a general curve, $S$ attains the Nakajima's upper bound $3(\\gamma-1)$ and $\\K(\\cX)$ is an unramified Galo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5108","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"}