{"paper":{"title":"Large $p$-groups of automorphisms of algebraic curves in characteristic $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G\\'abor Korchm\\'aros, Massimo Giulietti","submitted_at":"2015-07-14T06:44:03Z","abstract_excerpt":"Let $S$ be a $p$-subgroup of the $\\mathbb K$-automorphism group $Aut(\\mathcal X)$ of an algebraic curve $\\mathcal X$ of genus $g\\ge 2$ and $p$-rank $\\gamma$ defined over an algebraically closed field $\\mathbb{K}$ of characteristic $p\\geq 3$. Nakajima proved that if $\\gamma \\ge 2$ then $|S|\\leq \\textstyle\\frac{p}{p-2}(g-1)$. If equality holds, $\\mathcal X$ is a Nakajima extremal curve. We prove that if $$|S|>\\textstyle\\frac{p^2}{p^2-p-1}(g-1)$$ then one of the following cases occurs:\n  (i) $\\gamma=0$ and the extension $\\mathbb K(\\mathcal X)|\\mathbb K(\\mathcal X)^S$ completely ramifies at a uniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03737","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"}