Special subvarieties of Drinfeld modular varieties
Date
2010-11
Authors
Breuer, Florian
Journal Title
Journal ISSN
Volume Title
Publisher
Walter de Gruyter
Abstract
We explore an analogue of the Andr´e-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 which all lie in one Hecke orbit, and secondly when X is a curve containing
infinitely many CM points without any additional assumptions.
Description
Accepted for publication under copy editing
Keywords
Drinfeld modules, Drinfeld modular varieties, Special subvarieties, CM points, Andre-Oort, Hecke correspondence
Citation
Breuer, F. 2010. Special subvarieties of Drinfeld modular varieties. Journal fuer die reine und angewandte Mathematik.