Local-global principles for algebraic covers
type: Item
instance of: scholarly article
title: Local-global principles for algebraic covers
zbMATH Open document ID: 0915.12003
DOI: 10.1007/BF02762275
author: Pierre Dèbes
author: Jean-Claude Douai
published in: Israel Journal of Mathematics
publication date: 1999-04-25T00:00:00Z
review text: The authors consider the following: Let \(B\) be an algebraic variety defined over a number field \(K\) and \(f:X\to B\) a cover a priori defined over \(\overline K\). Suppose \(f\) can be defined over each completion of \(K_v\) of \(K\). Does it follow that \(f\) can be defined over \(K\)? The authors prove that the answer is affirmative under some conditions.
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 1250647
zbMATH Keywords: local-global principles
zbMATH Keywords: algebraic covers
zbMATH Keywords: algebraic variety
MaRDI profile type: Publication
cites work: Q5302599
cites work: Hurwitz families and arithmetic Galois groups
cites work: Q4849442
cites work: Algebraic covers: Field of moduli versus field of definition
cites work: Fields of definition of function fields and hurwitz families — groups as galois groups
cites work: Q5632701
cites work: Q3871006
cites work: Effective descent of the field of definition of a Galois cover
cites work: Cohomologie Galoisienne. Cours au College de France, 1962-1963. 4e ed
description: scientific article; zbMATH DE number 1250647