{"paper":{"title":"Large automorphism groups compared to the $p$-rank 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, Marco Timpanella, Massimo Giulietti","submitted_at":"2026-06-08T18:39:22Z","abstract_excerpt":"Let $\\cX$ be a (projective, geometrically irreducible, non-singular) algebraic curve of genus $\\ge 2$ and positive $p$-rank $\\gamma(\\cX)$, defined over an algebraically closed field $\\mathbb{K}$ of positive characteristic $p>0$. Contrary to what occurs for the genera, no function $h(\\gamma)$ exists such that $|\\aut(\\cX)|\\le h(\\gamma)$ whenever $\\gamma=\\gamma(\\cX)$. Thus, to have a bound on $|\\aut(\\cX)|$ only depending on $\\gamma(\\cX)$, some restrictions on $\\cX$ and $\\aut(\\cX)$ are needed. In this context, the following theorem is proven. Let $\\Gamma$ be a subgroup of $\\aut(\\cX)$. Assume the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10065","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10065/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}