Kucharczyk, Robert A.
- Journal Article
Rights / licenseCreative Commons Attribution-NonCommercial 3.0 Unported
We investigate modular embeddings for semi-arithmetic Fuchsian groups. First, we prove some purely algebro-geometric or even topological criteria for a regular map from a smooth complex curve to a quaternionic Shimura variety to be covered by a modular embedding. Then, we set up an adelic formalism for modular embeddings and apply our criteria to study the effect of abstract field automorphisms of C on modular embeddings. Finally, we derive that the absolute Galois group of Q operates on the dessins d’enfants defined by principal congruence subgroups of (arithmetic or nonarithmetic) triangle groups by permuting the defining ideals in the tautological way. Show more
Journal / seriesAlgebraic Geometry
Pages / Article No.
PublisherEuropean Mathematical Society
Subjectmodular embeddings; Fuchsian group; Hilbert–Blumenthal varieties; automorphic vector bundles; dessins d’enfants
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