The Andr\'e-Oort Conjecture for Drinfeld Modular Varieties

TL;DR

This paper proves an analogue of the Andre9-Oort conjecture for Drinfeld modular varieties, establishing the distribution of special points with separable reflex fields using adapted classical methods.

Contribution

It extends the Andre9-Oort conjecture to Drinfeld modular varieties for special points with separable reflex fields, adapting methods from classical cases.

Findings

Proves the conjecture for special points with separable reflex fields.

Extends previous results to higher-dimensional varieties.

Adapts classical proof techniques to the function field setting.

Abstract

We consider the analogue of the Andr\'e-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 Andr\'e-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.