Unramified extensions over low degree number fields

DOI10.1016/j.jnt.2019.10.021zbMath1470.11293arXiv1901.03985OpenAlexW2989564149MaRDI QIDQ2307444

Danny Neftin, Joachim König, Jack Sonn

Publication date: 27 March 2020

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

Full work available at URL: https://arxiv.org/abs/1901.03985

zbMATH Keywords

bounded ramificationGalois theoryunramified extensionsspecialization of Galois covers

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Galois theory (11R32)

Related Items (7)

Quadratic number fields with unramified \(\mathrm{SL}_2(5)\)-extensions ⋮ On -unramified extensions over imaginary quadratic fields ⋮ Non-principal Euclidean ideal class in a family of biquadratic fields with the class number two ⋮ On Galois extensions with prescribed decomposition groups ⋮ On number fields with power-free discriminant ⋮ ON UNRAMIFIED SOLVABLE EXTENSIONS OF SMALL NUMBER FIELDS ⋮ Unramified extensions of quadratic number fields with certain perfect Galois groups

Cites Work

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• Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
• On rational functions with monodromy group \(M_{11}\)
• Extensions régulières de \({\mathbb{Q}}(T)\) de groupe de Galois \(\tilde A_ n\). (Regular extensions of \({\mathbb{Q}}(T)\) with Galois group \(\tilde A_ n)\)
• Construction of unramified extensions with a prescribed Galois group
• Tame \(A_{n}\)-extensions of \({\mathbb Q}\)
• Unramified subextensions of ray class towers
• Chevalley-Weil theorem and subgroups of class groups
• Nonabelian Cohen-Lenstra moments
• Computation of some moduli spaces of covers and explicit \({\mathcal S}_n\) and \({\mathcal A}_n\) regular \({\mathbb Q}(T)\)-extensions with totally real fibers.
• Algebraic number fields with the discriminant equal to that of a quadratic number field
• Embedding problems over large fields
• Galois covers of \(\mathbb P^1\) over \(\mathbb Q\) with prescribed local or global behavior by specialization
• Heuristics for \(p\)-class towers of imaginary quadratic fields
• Construction of maximal unramified \(p\)-extensions with prescribed Galois groups
• On unramified Galois extensions of quadratic number fields
• A construction of polynomials with squarefree discriminants
• Galois realizations with inertia groups of order two
• Non-abelian Cohen–Lenstra heuristics over function fields
• SIEVES AND THE MINIMAL RAMIFICATION PROBLEM
• On extensions of number fields obtained by specializing branched coverings.

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