SU\G(𝔸)/K·U

Special subvarieties of Drinfeld modular varieties

Florian Breuer

Type: Article

Publication Date: 2011-09-12

Citations: 13

DOI: https://doi.org/10.1515/crelle.2011.136

Abstract

We explore an analogue of the André–Oort Conjecture for subvarieties of Drinfeld modular varieties. The conjecture states that a subvariety X of a Drinfeld modular variety contains a Zariski-dense set of complex multiplication (CM) points if and only if X is a “special” subvariety (i.e. X is defined by requiring additional endomorphisms). We prove this conjecture in two cases: firstly when X contains a Zariski-dense set of CM points all of which lie in one Hecke orbit, and secondly when X is a curve containing infinitely many CM points without any additional assumptions.

Locations

  • arXiv (Cornell University) - View - PDF
  • Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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Works Cited by This (25)

Action Title Year Authors
+ Sous-variétés d’une variété abélienne et points de torsion 1983 Michel Raynaud
+ PDF Chat On the André-Oort Conjecture for Hilbert Modular Surfaces 2001 Bas Edixhoven
+ CM points on products of Drinfeld modular curves 2006 Florian Breuer
+ Special points on products of modular curves 2005 Bas Edixhoven
+ G-functions and geometry 1989 Yves André
+ PDF Chat None 1998 Bas Edixhoven
+ None 1998 Igor Yu. Potemine
+ PDF Chat None 1998 B.J. Moonen
+ PDF Chat on a result of moonen on the moduli space of principally polarised abelian varieties 2005 Andrei Yafaev
+ PDF Chat The André-Oort conjecture 2014 Bruno Klingler
Andrei Yafaev