Analytic lifting of algebraic tori
type: Item
instance of: scholarly article
title: Analytic lifting of algebraic tori
zbMATH Open document ID: 0605.14038
DOI: 10.1007/BF01451408
author: Peter Ullrich
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164056
review text: Let \(G\) be an analytic group over a complete nonarchimedean field \(k\) and let \(\bar G\) be the algebraic group over the residue field \(\bar k\) of \(k\) which is the reduction of \(G\). The author proves that an affine closed subtorus \(\bar T\) of \(\bar G\) can be lifted to a closed affinoid subtorus \(T\) of \(G\) if \(\bar T\) is \(k\)-split and \(G\) is smooth over the valuation ring of \(k\). The proof uses a rigid-analytic shrinking technique to reduce to the case \(\bar G={\bar {\mathbb G}}^ d_ m\times {\bar {\mathbb G}}^ r_ a\).
reviewed by: Frank Herrlich
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 32P05
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 3977166
zbMATH Keywords: lifting of algebraic subtori
zbMATH Keywords: analytic group over a complete nonarchimedean field
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3977166