Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture

Emmanuel Ullmo, Andrei Yafaev

Type: Article

Publication Date: 2014-07-22

Citations: 52

DOI: https://doi.org/10.4007/annals.2014.180.3.1

Abstract

In this paper we develop a strategy and some technical tools for proving the André-Oort conjecture.We give lower bounds for the degrees of Galois orbits of geometric components of special subvarieties of Shimura varieties, assuming the Generalised Riemann Hypothesis.We proceed to show that sequences of special subvarieties whose Galois orbits have bounded degrees are equidistributed in a suitable sense.

Locations

Annals of Mathematics - View - PDF

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Works Cited by This (25)

Action	Title	Year	Authors
+	Arithmetical compactification of mixed Shimura varieties	1990	Richard Pink
+	Models of Shimura varieties in mixed characteristics	1998	B.J. Moonen
+	Travaux de Shimura	1971	Pierre Deligne
+	Reductive groups over local fields	1979	Jacques Tits
+	Special points on products of modular curves	2005	Bas Edixhoven
+ PDF Chat	None	1998	B.J. Moonen
+	On the Kodaira dimension of the Siegel modular variety	1983	David Mumford
+	Introduction to Shimura Varieties	2004	J. S. Milne
+ PDF Chat	on a result of moonen on the moduli space of principally polarised abelian varieties	2005	Andrei Yafaev
+	Algebraic groups and number theory	1992	В. П. Платонов Andrei S. Rapinchuk