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UID:5564@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140213T110000
DTEND;TZID=Europe/Paris:20140213T120000
DTSTAMP:20241030T162049Z
URL:https://www.i2m.univ-amu.fr/evenements/on-computing-belyi-maps/
SUMMARY:Jeroen Sijsling (...): On computing Belyi maps
DESCRIPTION:Jeroen Sijsling: A Belyi map is a finite morphism to the comple
 x projective line that is ramified above at most three points. Surprisingl
 y\, the algebraic curves that admit a Belyi map are exactly those that are
  defined over the algebraic closure of QQ . Due to the simple combinatoria
 l description of covers as finite sets with an action of the fundamental g
 roup\, the theory of Belyi maps therefore gives a way to study the absolut
 e Galois group of QQ\, one of Grothendieck’s dreams.\nThis talk focuses 
 on the efforts so far to compute Belyi maps explicitly.\nThe currently ava
 ilable techniques are described\, including a recent one due to Voight et 
 al. that uses modular functions. Many asides are explored\, such as Galois
  Belyi maps and questions concerning field of definition. http://arxiv.org
 /abs/1311.2529\n\nJeroen Sijsling\, Institut für Reine Mathematik at the 
 Universität Ulm
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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