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The André–Oort conjecture for Drinfeld modular varieties

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  14 February 2013

Patrik Hubschmid
Patrik Hubschmid*
Affiliation:
Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany (email: patrik.hubschmid@iwr.uni-heidelberg.de)
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Abstract

We consider the analogue of the André–Oort conjecture for Drinfeld modular varieties which was formulated by Breuer. We prove this analogue for special points with separable reflex field over the base field by adapting methods which were used by Klingler and Yafaev to prove the André–Oort conjecture under the generalized Riemann hypothesis in the classical case. Our result extends results of Breuer showing the correctness of the analogue for special points lying in a curve and for special points having a certain behaviour at a fixed set of primes.

Keywords

Drinfeld modular varietiesAndré–Oort conjecture

MSC classification

Secondary: 11G09: Drinfel'd modules; higher-dimensional motives, etc. 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 4 , April 2013 , pp. 507 - 567
Copyright
Copyright © 2013 The Author(s)

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