
Open access
Author
Date
2018-03Type
- Journal Article
Abstract
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
Permanent link
https://doi.org/10.3929/ethz-b-000260986Publication status
publishedExternal links
Journal / series
Algebraic GeometryVolume
Pages / Article No.
Publisher
European Mathematical SocietySubject
modular embeddings; Fuchsian group; Hilbert–Blumenthal varieties; automorphic vector bundles; dessins d’enfantsMore
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