Higher Newton polygons and integral bases

DOI10.1016/j.jnt.2014.07.027zbMath1394.11071OpenAlexW2963033659MaRDI QIDQ472859

Jesús Montes, Jordi Guárdia i Rúbies, Enric Nart Viñals

Publication date: 20 November 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.07.027

zbMATH Keywords

Newton polygonDedekind domainlocal fieldglobal field\(p\)-integral basesmontes algorithmreduced bases

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Algebraic number theory computations (11Y40) Algebraic numbers; rings of algebraic integers (11R04) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (19)

Computation of integral bases ⋮ On Higher Congruences Between Cusp Forms and Eisenstein Series. II. ⋮ Class numbers of large degree nonabelian number fields ⋮ Explicit integral basis of \(\mathbb{Q}(\sqrt[p_1 p_2{a})\)] ⋮ Monogenic fields arising from trinomials ⋮ A new computational approach to ideal theory in number fields ⋮ Square-free OM computation of global integral bases ⋮ Triangular bases of integral closures ⋮ Computation of triangular integral bases ⋮ Two families of monogenic $S_4$ quartic number fields ⋮ Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields ⋮ Newton polygons of higher order in algebraic number theory ⋮ Discriminants of simplest \(3^n\)-tic extensions ⋮ On the equivalence of types ⋮ Okutsu-Montes representations of prime ideals of one-dimensional integral closures ⋮ How far is an extension of \(p\)-adic fields from having a normal integral basis? ⋮ Computing zeta functions of algebraic curves using Harvey's trace formula ⋮ On the discriminant of pure number fields ⋮ Discriminants of Chebyshev radical extensions

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• Complexity of OM factorizations of polynomials over local fields
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• Computing local integral closures
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