A family of Eisenstein polynomials generating totally ramified extensions, identification of extensions and construction of class fields

DOI10.1142/S1793042114500511zbMath1318.11155arXiv1109.4617MaRDI QIDQ3191215

Maurizio Monge

Publication date: 30 September 2014

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

Full work available at URL: https://arxiv.org/abs/1109.4617

zbMATH Keywords

algorithmlocal class field theoryEisenstein polynomial

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Ramification and extension theory (11S15) Class field theory; (p)-adic formal groups (11S31) Polynomials (11S05)

Related Items (5)

EISENSTEIN POLYNOMIALS DEFINING CYCLIC p-ADIC FIELDS WITH MINIMAL WILD RAMIFICATION ⋮ AUTOMORPHISMS OF 2-ADIC FIELDS OF DEGREE TWICE AN ODD NUMBER ⋮ Enumerating extensions of (π)-adic fields with given invariants ⋮ ON GALOIS p-ADIC FIELDS OF p-POWER DEGREE ⋮ Degree 12 2-adic fields with automorphism group of order 4

Cites Work

• Unnamed Item
• New numerical invariants for totally ramified extensions of local fields
• A database of local fields
• Constructing class fields over local fields
• On the computation of all extensions of a 𝑝-adic field of a given degree
• An ultrametric space of Eisenstein polynomials and ramification theory
• RAMIFICATION POLYGONS, SPLITTING FIELDS, AND GALOIS GROUPS OF EISENSTEIN POLYNOMIALS
• 𝑝-adic Power Series which Commute under Composition
• On the ramification breaks
• Newton polygons of higher order in algebraic number theory

This page was built for publication: A family of Eisenstein polynomials generating totally ramified extensions, identification of extensions and construction of class fields