Algebraically closed descent
type: Item
instance of: scholarly article
title: Algebraically closed descent
zbMATH Open document ID: 1042.12003
DOI: 10.1016/S0021-8693(03)00305-3
author: Geoffroy Derome
published in: Journal of Algebra
publication date: 2003-09-07T00:00:00Z
review text: The following theorem is proved: Let \(K/k\) be an extension of algebraically closed fields of infinite transcendence degree, and let \(Y\) be a \(\text{Spec}(k)\)-scheme. If \(X\) is an integral \(Y_K\)-scheme of finite type such that \(X^\sigma \cong_{Y_K} X\) for all \(\sigma\in \Aut_k(K)\), then \(X\) admits a unique \(Y\)-model.
reviewed by: Roberto Dvornicich
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 14E20
zbMATH DE Number: 1975849
zbMATH Keywords: Field of moduli
zbMATH Keywords: Field of definition
zbMATH Keywords: Fibered product
zbMATH Keywords: Going-up theorem
zbMATH Keywords: Hilbert's Nullstellensatz
MaRDI profile type: Publication
cites work: Q4422456
cites work: Algebraic covers: Field of moduli versus field of definition
cites work: Q4317713
cites work: Fields of definition of function fields and hurwitz families — groups as galois groups
cites work: Q4143433
cites work: Q4003835
cites work: Q4364760
full work available at URL: s0021-8693(03)00305-3
OpenAlex ID: W2082516235
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description: scientific article; zbMATH DE number 1975849