2005/03/22 by Florian Breuer, Breuer, Florian
Mathematics · #11G09 #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G09 #msc:14G35
paper · pdf · doi:10.48550/arxiv.math/0503452
22 pages, significant rewrite
arxiv created 2009/02/28 · arxiv updated 2009/12/01
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 with a certain behaviour above a fixed prime (which is the case if these CM points lie in one Hecke orbit), and secondly when X is a curve containing infinitely many CM points without any additional assumptions.