Constructing unramified extensions over quadratic fields

Aoki, Misato; Kida, Masanari

doi:10.2140/involve.2022.15.55

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Constructing unramified extensions over quadratic fields

Misato Aoki and Masanari Kida

Vol. 15 (2022), No. 1, 55–68

DOI: 10.2140/involve.2022.15.55

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

Vol. 15, No. 1, 2022