{"paper":{"title":"Generalized Artin-Mumford curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Zini, Maria Montanucci","submitted_at":"2016-12-06T10:07:08Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be the finite field of order $q=p^h$ with $p>2$ prime and $h>1$, and let $\\mathbb{F}_{\\bar{q}}$ be a subfield of $\\mathbb{F}_q$. From any two $\\bar{q}$-linearized polynomials $L_1,L_2 \\in \\overline{\\mathbb{F}}_q[T]$ of degree $q$, we construct an ordinary curve $\\mathcal{X}_{(L_1,L_2)}$ of genus $(q-1)^2$ which is a generalized Artin-Schreier cover of the projective line $\\mathbb{P}^1$. The automorphism group of $\\mathcal{X}_{(L_1,L_2)}$ over the algebraic closure $\\overline{\\mathbb{F}}_q$ of $\\mathbb{F}_q$ contains a semidirect product $\\Sigma \\rtimes \\Gamma$ of an elementa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01731","kind":"arxiv","version":3},"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"}