Galois orbits and equidistribution: Manin-Mumford and André-Oort
type: Item
instance of: scholarly article
title: Galois orbits and equidistribution: Manin-Mumford and André-Oort
zbMATH Open document ID: 1209.11055
author: Andrei Yafaev
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2009-10-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10894
review text: In this review article, the author outlines a similar proof of the Manin-Mumford conjecture and the André-Oort conjecture. This proof is based on a ``Galois theory -- ergodic theory alternative''. In the case of the Manin-Mumford conjecture, it is due to \textit{N. Ratazzi} and \textit{E. Ullmo} [``Galois + equidistribution = Manin-Mumford'', Clay Math. Proc. 8, 419--430 (2009; Zbl 1250.11062)] and in the case of the André-Oort conjecture, it is due to B. Klingler, E. Ullmo and A. Yafaev [``On the André-Oort conjecture for products of modular curves.'', Clay Math. Proc. 8, 431--439 (2009; Zbl 1254.11062); B. Klingler and A. Yafaev, ``Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture'', preprint \url{http:www.institut.math.jussieu.fr/~klingler/papiers/KY12.pdf}].
reviewed by: Benoît Stroh
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 37P99
Mathematics Subject Classification ID: 14K12
zbMATH DE Number: 5620664
zbMATH Keywords: Manin-Mumford conjecture
zbMATH Keywords: André-Oort conjecture
zbMATH Keywords: abelian varieties
zbMATH Keywords: Shimura varieties
zbMATH Keywords: special points
zbMATH Keywords: equidistribution
MaRDI profile type: Publication
OpenAlex ID: W2335721773
cites work: Special subvarieties of Drinfeld modular varieties
cites work: Equidistribution of special subvarieties
cites work: Q3877792
cites work: The André-Oort conjecture
cites work: Q3655925
cites work: Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture
cites work: A Combination of the Conjectures of Mordell-Lang and André-Oort
cites work: The Manin-Mumford Conjecture: A Brief Survey
cites work: A conjecture of Yves André's
DOI: 10.5802/JTNB.684
description: scientific article; zbMATH DE number 5620664