A maximal curve which is not a Galois subcover of the Hermitian curve

DOI10.1007/s00574-006-0008-zzbMath1118.14033OpenAlexW2057660477MaRDI QIDQ2507560

Arnaldo Garcia, Henning Stichtenoth

Publication date: 4 October 2006

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-006-0008-z

zbMATH Keywords

finite fieldsrational pointsGalois coveringsHermitian curvesmaximal curves

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Counting solutions of Diophantine equations (11D45) Curves over finite and local fields (11G20)

Related Items (20)

Maximal curves from subcovers of the GK-curve ⋮ Weierstrass semigroups for maximal curves realizable as Harbater-Katz-Gabber covers ⋮ Some Ree and Suzuki curves are not Galois covered by the Hermitian curve ⋮ On maximal curves which are not Galois subcovers of the Hermitian curve ⋮ On the number of rational points on Artin-Schreier hypersurfaces ⋮ A birational embedding with two Galois points for quotient curves ⋮ A note on certain maximal curves ⋮ On additive polynomials and certain maximal curves ⋮ An \(\mathbb{F}_{p^2 } \)-maximal Wiman sextic and its automorphisms ⋮ A new family of maximal curves over a finite field ⋮ On maximal curves that are not quotients of the Hermitian curve ⋮ On the spectrum for the genera of maximal curves over small fields ⋮ On the spectrum of genera of quotients of the Hermitian curve ⋮ The complete list of genera of quotients of the \(\mathbb{F}_{q^2}\)-maximal Hermitian curve for \(q \equiv 1 \pmod 4\) ⋮ Further examples of maximal curves ⋮ On the curve \(y^n = x^m + x\) over finite fields ⋮ The curve \(y^n=x^\ell(x^m+1)\) over finite fields. II ⋮ ON QUOTIENT CURVES OF THE FERMAT CURVE OF DEGREE TWELVE ATTAINING THE SERRE BOUND ⋮ On the classification problem for the genera of quotients of the Hermitian curve ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve

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