Geodesic
Finiteness results for Teichmüller curves
[Résultats de finitude pour les courbes de Teichmüller]
Möller, Martin1
1 Universität Essen FB 6 (Mathematik) 45117 Essen (Germany)
Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 63-83.

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We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C, such that (i) C lies in the hyperelliptic locus and (ii) C is generated by an abelian differential with two zeros of order g-1. We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.

Pour chaque genre g fixé, on montre qu’il n’y a qu’un nombre fini de courbes de Teichmüller C algébriquement primitives telles que (i) C appartient au lieu hyperelliptique et (ii) C est engendrée par une différentielle abélienne avec deux zéros d’ordre g-1. On montre en outre que pour ces courbes de Teichmüller le corps de traces du groupe affine n’est pas seulement totalement réel mais cyclotomique.

DOI : 10.5802/aif.2344
Classification : 14D07, 32G20
Keywords: Teichmüller curves, cyclotomic field, Neron model
Mots-clés : courbes de Teichmüller, corps cyclotomiques, modèle de Neron

Möller, Martin 1

1 Universität Essen FB 6 (Mathematik) 45117 Essen (Germany) 
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Möller, Martin. Finiteness results for Teichmüller curves. Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 63-83. doi : 10.5802/aif.2344. http://geodesic.mathdoc.fr/articles/10.5802/aif.2344/

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