RAMIFICATION POLYGONS, SPLITTING FIELDS, AND GALOIS GROUPS OF EISENSTEIN POLYNOMIALS

DOI10.1142/S1793042112500832zbMath1286.11201MaRDI QIDQ2907090

Sebastian Pauli, Christian Greve

Publication date: 6 September 2012

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

zbMATH Keywords

local fieldsGalois groupNewton polygonsEisenstein polynomialsramification polygons

Mathematics Subject Classification ID

Galois theory (11S20) Ramification and extension theory (11S15)

Related Items (8)

A family of Eisenstein polynomials generating totally ramified extensions, identification of extensions and construction of class fields ⋮ Enumerating extensions of (π)-adic fields with given invariants ⋮ 3-torsion and conductor of genus 2 curves ⋮ A characterization of Eisenstein polynomials generating extensions of degree \(p^2\) and cyclic of degree \(p^3\) over an unramified \(\mathfrak p\)-adic field ⋮ The first digit of the discriminant of Eisenstein polynomials as an invariant of totally ramified extensions of \(p\)-adic fields ⋮ Computing the Galois group of a polynomial over a p-adic field ⋮ Jump sets in local fields ⋮ Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

Cites Work

• Unnamed Item
• Single-factor lifting and factorization of polynomials over local fields
• Octic 2-adic fields
• Computing Galois groups over the rationals
• On a theorem of Ore
• The Magma algebra system. I: The user language
• A fast algorithm for polynomial factorization over \(\mathbb Q_p\)
• A database of local fields
• The Ramification Polygon for Curves over a Finite Field
• Newton polygons of higher order in algebraic number theory

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