Titlebook: Dessins d‘Enfants on Riemann Surfaces; Gareth A. Jones,Jürgen Wolfart Book 2016 Springer International Publishing Switzerland 2016 Dessins

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Arithmetic Aspectstheoretic criterion for elliptic curves (those of genus 1) to have complex multiplication, that is, to have non-trivial endomorphisms. This criterion relies on a very special property of curves and dessins of genus 1, that they have infinitely many unramified self-coverings.

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Dessins and Triangle Groupsn mapping theorem. We describe the classification of cocompact Fuchsian groups, and the local and global properties of quotients of the hyperbolic plane by such groups. We discuss the inclusion relations between these groups, classified by Singerman, giving particular attention to triangle groups. T

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Galois Actionsunction fields. The latter examples provide a link between Galois groups and covering groups for regular coverings. Another important example is the absolute Galois group ., the automorphism group of the field of all algebraic numbers: as the projective limit of the (finite) Galois groups of the Gal