Hyperbolicity, automorphic forms and Siegel modular varieties

Erwan Rousseau (1)

1 I2M - Institut de Mathématiques de Marseille

We study the hyperbolicity of compactifications of quotients of bounded symmetric domains by arithmetic groups. We prove that, up to an étale cover, they are Kobayashi hyperbolic modulo the boundary. Applying our techniques to Siegel modular varieties, we improve some former results of Nadel on the non-existence of certain level structures on abelian varieties over complex function fields.

Mots clés: Siegel modular varieties; automorphic forms; level structures; Kobayashi hyperbolicity; bounded symmetric domains

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Erwan Rousseau. Hyperbolicity, automorphic forms and Siegel modular varieties. Annales Scientifiques de l'École Normale Supérieure, 2016, 49 (1), pp.249-255. ⟨10.24033/asens.2281⟩. ⟨hal-00790243v2⟩