Presentation
Quasi-platonic actions of PSL2(q) and their dessins
Central Section AMS Regional Meeting
(2015)
Abstract
A quasi-platonic action of the group G on the Riemann surface S is a conformal action of G on S such that S/G is a sphere and the projection S→S/G is branched over three points. In this talk we describe the quasi-platonic actions of PSL(2, q). Quasi-platonic actions are interesting since each surface with a quasi-platonic action must have a defining equation with coefficients in a number field. Additionally, each quasi-platonic action defines a regular dessin d’enfant on S, namely an embedded bipartite graph whose complement is a collection of rotationally symmetric, hyperbolic polygons.The group G is an automorphism group of the dessin. The absolute Galois group acts on the set of all dessins by acting on the coefficients of the defining equation of S. We discuss the Galois action on the dessins arising from quasi-platonic actions of PSL(2,q).
Keywords
- Riemann surface,
- quasi-platonic action,
- dessin d’enfant,
- absolute Galois group
Disciplines
Publication Date
March 14, 2015
Location
East Lansing, MI
Citation Information
Sean A Broughton. "Quasi-platonic actions of PSL2(q) and their dessins" Central Section AMS Regional Meeting (2015) Available at: http://works.bepress.com/allen_broughton/59/
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