Vol. 15, No. 1, 2022

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Constructing unramified extensions over quadratic fields

Misato Aoki and Masanari Kida

Vol. 15 (2022), No. 1, 55–68
Abstract

Using some regular polynomials with prescribed Galois groups, we construct explicit infinite families of unramified extensions over quadratic fields by specializations satisfying certain congruence conditions.

Keywords
unramified extension, quadratic field, regular extension
Mathematical Subject Classification 2010
Primary: 12F12, 11R09, 11R32
Milestones
Received: 15 March 2020
Revised: 2 April 2021
Accepted: 9 August 2021
Published: 14 March 2022

Communicated by Filip Saidak
Authors
Misato Aoki
Tokyo University of Science
Tokyo
Japan
Masanari Kida
Department of Mathematics, Faculty of Science Division I
Tokyo University of Science
Tokyo
Japan