Hyperbolicity, automorphic forms and Siegel modular varieties

2013/02/19 by Rousseau, Erwan
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1302.4723

Abstract

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.

Related

• Hyperbolicity of singular spaces
• A strong hyperbolicity property of locally symmetric varieties
• Subvarieties of quotients of bounded symmetric domains
• Fundamental group of locally symmetric varieties
• Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms