Enumerating extensions of (π)-adic fields with given invariants

DOI10.1142/S1793042117501081zbMath1427.11129arXiv1504.06671OpenAlexW2963796527MaRDI QIDQ5357488

Brian Sinclair, Sebastian Pauli

Publication date: 8 September 2017

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

Full work available at URL: https://arxiv.org/abs/1504.06671

zbMATH Keywords

\(p\)-adic fieldlocal 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)

Related Items (4)

AUTOMORPHISMS OF 2-ADIC FIELDS OF DEGREE TWICE AN ODD NUMBER ⋮ 3-torsion and conductor of genus 2 curves ⋮ ON GALOIS p-ADIC FIELDS OF p-POWER DEGREE ⋮ Computing the Galois group of a polynomial over a p-adic field

Uses Software

• Magma

Cites Work

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• A family of Eisenstein polynomials generating totally ramified extensions, identification of extensions and construction of class fields
• The Local Kronecker-Weber Theorem
• The Ramification Polygon for Curves over a Finite Field
• Factoring Polynomials over Local Fields II

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