{"paper":{"title":"Large odd prime power order automorphism groups of algebraic curves in any characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G\\'abor Korchm\\'aros, Maria Montanucci","submitted_at":"2018-10-17T12:54:54Z","abstract_excerpt":"Let $\\mathcal{X}$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \\ge 2$ defined over an algebraically closed field $\\mathbb{K}$ of odd characteristic $p\\ge 0$, and let $\\rm{Aut}(\\mathcal{X})$ be the group of all automorphisms of $\\mathcal{X}$ which fix $\\mathbb{K}$ element-wise. For any a subgroup $G$ of $\\rm{Aut}(\\mathcal{X})$ whose order is a power of an odd prime $d$ other than $p$, the bound proven by Zomorrodian for Riemann surfaces is $|G|\\leq 9(g-1)$ where the extremal case can only be obtained for $d=3$. We prove Zomorrodian's result for any $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07506","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"}