Asymptotics of Reduced Algebraic Curves Over Finite Fields

DOI10.1007/978-3-319-96827-8_22zbMath1425.14020OpenAlexW2890074667MaRDI QIDQ4613707

José I. Farrán

Publication date: 24 January 2019

Published in: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-96827-8_22

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Applications to coding theory and cryptography of arithmetic geometry (14G50) Combinatorial codes (94B25)

Uses Software

• SINGULAR
• brnoeth.lib

Cites Work

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• Number of points of an algebraic curve
• Algebroid curves in positive characteristic
• On towers and composita of towers of function fields over finite fields
• Plane curves of minimal degree with prescribed singularities
• Irreducibility criterion for germs of analytic functions of two complex variables
• Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• The Newton polygon of plane curves with many rational points

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