%0 Journal Article %T Hyperbolicity, automorphic forms and Siegel modular varieties %+ Institut de Mathématiques de Marseille (I2M) %A Rousseau, Erwan %< avec comité de lecture %@ 0012-9593 %J Annales Scientifiques de l'École Normale Supérieure %I Société mathématique de France %V 49 %N 1 %P 249-255 %8 2016 %D 2016 %Z 1302.4723 %R 10.24033/asens.2281 %K Siegel modular varieties %K automorphic forms %K level structures %K Kobayashi hyperbolicity %K bounded symmetric domains %Z 32Q45; 32M15; 11G99; 14K15 %Z Mathematics [math]/Algebraic Geometry [math.AG] %Z Mathematics [math]/Complex Variables [math.CV]Journal articles %X 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. %G English %2 https://hal.science/hal-00790243v2/document %2 https://hal.science/hal-00790243v2/file/quotients.pdf %L hal-00790243 %U https://hal.science/hal-00790243 %~ CNRS %~ UNIV-AMU %~ EC-MARSEILLE %~ INSMI %~ I2M %~ I2M-2014-