{"paper":{"title":"Some Ree and Suzuki curves are not Galois covered by the Hermitian curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Giovanni Zini, Maria Montanucci","submitted_at":"2016-03-22T08:36:50Z","abstract_excerpt":"The Deligne-Lusztig curves associated to the algebraic groups of type $^2A_2$, $^2B_2$, and $^2G_2$ are classical examples of maximal curves over finite fields. The Hermitian curve $\\mathcal H_q$ is maximal over $\\mathbb F_{q^2}$, for any prime power $q$, the Suzuki curve $\\mathcal S_q$ is maximal over $\\mathbb F_{q^4}$, for $q=2^{2h+1}$, $h\\geq1$ and the Ree curve $\\mathcal R_q$ is maximal over $\\mathbb F_{q^6}$, for $q=3^{2h+1}$, $h\\geq0$. In this paper we show that $\\mathcal S_8$ is not Galois covered by $\\mathcal H_{64}$. We also give a proof for an unpublished result due to Rains and Ziev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06706","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"}