Curves of every genus with many points. II: Asymptotically good families

DOI10.1215/S0012-7094-04-12224-9zbMath1072.11041arXivmath/0208060OpenAlexW3098590634MaRDI QIDQ707493

Joseph L. Wetherell, Noam D. Elkies, Everett W. Howe, Bjorn Poonen, Michael E. Zieve, Andrew Kresch

Publication date: 9 February 2005

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0208060

zbMATH Keywords

class field towersasymptotic lower boundscurves over finite fields with many rational pointsdegree-2 covering of curves

Mathematics Subject Classification ID

Rational points (14G05) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15)

Related Items (10)

Curves of every genus with a prescribed number of rational points ⋮ Lattices with exponentially large kissing numbers ⋮ Lower bounds on the maximal number of rational points on curves over finite fields ⋮ Curves of fixed gonality with many rational points ⋮ Curves with a prescribed number of rational points ⋮ On the number of points on abelian and Jacobian varieties over finite fields ⋮ Semiample Bertini theorems over finite fields ⋮ On the Euler-Kronecker constants of global fields and primes with small norms ⋮ New lower bounds for the Ihara function \(A(q)\) for small primes ⋮ Curves of every genus with many points. I: Abelian and toric families.

Cites Work

• Algebraic function fields and codes
• Algebraic curves over \({\mathbb{F}}_ 2\) with many rational points
• On towers and composita of towers of function fields over finite fields
• On the asymptotic behaviour of some towers of function fields over finite fields
• Curves of every genus with many points. I: Abelian and toric families.
• Reduction modulo P of Shimura curves
• Coverings of curves with asymptotically many rational points
• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• Arithmetic of unitary groups
• On canonical models of arithmetic quotients of bounded symmetric domains
• Bertini theorems over finite fields
• On the Riemann Hypothesis in Function-Fields
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