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VOL. 63 | 2012 Twisted covers and specializations
Pierre Dèbes, François Legrand

Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa

Abstract

The central topic is this question: is a given $k$-étale algebra $\prod_l E_l/k$ the specialization of a given $k$-cover $f : X \to B$ at some unramified point $t_0 \in B(k)$? Our main tool is a twisting lemma that reduces the problem to finding $k$-rational points on a certain $k$-variety. Previous forms of this twisting lemma are generalized and unified. New applications are given: a Grunwald form of Hilbert's irreducibility theorem over number fields, a non-Galois variant of the Tchebotarev theorem for function fields over finite fields, some general specialization properties of covers over PAC or ample fields.

Information

Published: 1 January 2012
First available in Project Euclid: 24 October 2018

zbMATH: 1321.11114
MathSciNet: MR3051242

Digital Object Identifier: 10.2969/aspm/06310141

Subjects:
Primary: 11R58, 12E25, 12E30, 14G05, 14H30
Secondary: 12Fxx, 14GXX

Rights: Copyright © 2012 Mathematical Society of Japan

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