Hyperbolic Ax-Lindemann theorem in the cocompact case

Abstract

We prove an analogue of the classical Ax-Lindemann theorem in the context of compact Shimura varieties. Our work is motivated by J. Pila's strategy for proving the André-Oort conjecture unconditionally

To appear in Duke Mathematical Journal

References in corpus (2)

• The Andre-Oort conjecture for the moduli space of Abelian Surfaces
• Definability of restricted theta functions and families of abelian varieties

Cited by in corpus (6)

• A non-archimedean Ax-Lindemann theorem
• Heights of pre-special points of Shimura varieties
• The space of homogeneous probability measures on ${\overline{\Gamma \backslash X}}_{\max }^S$ is compact
• Asymptotic total geodesy of local holomorphic curves exiting a bounded symmetric domain and applications to a uniformization problem for algebraic subsets
• Inner Galois Equidistribution in S-Hecke orbits
• Holomorphic curves in mixed Shimura varieties