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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.01731","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-06T10:07:08Z","cross_cats_sorted":[],"title_canon_sha256":"71a1c6dcf3031d6163455764a61cc1af745711d9a640bb718dbb0dc502c950a1","abstract_canon_sha256":"18acbbc7d84d521fef29cb801f1de5f2bce7e78f131591aca788fe4f95f398ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:29.674406Z","signature_b64":"PXtF3cOA0I24xTUNW23Zsp3p7EtKmN5a9RMRe4VL2DmaiA0FmC4hXq/x0kMFKq9EnMYfTFX0/3oeWy5w4muMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d9f1106dc4412fcd2ec38c9bcf1e99e7b58b34e25348b3caf32b7474e8565c2","last_reissued_at":"2026-05-18T00:43:29.673732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:29.673732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{P}^1$. 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