An Explicit Treatment of Cubic Function Fields with Applications

DOI10.4153/CJM-2010-032-0zbMath1213.14053OpenAlexW2045882129MaRDI QIDQ3580061

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Publication date: 11 August 2010

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/cjm-2010-032-0

zbMATH Keywords

class numberdiscriminantintegral basisnon-singularitycubic function fieldsignature of a place

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Special algebraic curves and curves of low genus (14H45) Curves over finite and local fields (11G20) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Applications to coding theory and cryptography of arithmetic geometry (14G50) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (6)

The geometry of the moduli space of non-cyclic biquadratic field extensions ⋮ Construction of all cubic function fields of a given square-free discriminant ⋮ Cubic function fields with prescribed ramification ⋮ An explicit triangular integral basis for any separable cubic extension of a function field ⋮ Tabulation of cubic function fields via polynomial binary cubic forms ⋮ A complete study of the ramification for any separable cubic global function field

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