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Special subvarieties of Drinfeld modular varieties
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Florian Breuer
Published/Copyright:
September 12, 2011
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.
Received: 2009-02-28
Revised: 2010-11-24
Published Online: 2011-09-12
Published in Print: 2012-07
©[2012] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Overconvergent Witt vectors
- Special subvarieties of Drinfeld modular varieties
- Explicit uniform estimation of rational points I. Estimation of heights
- Explicit uniform estimation of rational points II. Hypersurface coverings
- Pieri rules for the K-theory of cominuscule Grassmannians
- The Hörmander multiplier theorem for multilinear operators
- Quantum cluster variables via Serre polynomials
- Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
- On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
