Finiteness results for Teichmüller curves
Annales de l'Institut Fourier, Volume 58 (2008) no. 1, p. 63-83

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 : https://doi.org/10.5802/aif.2344
Classification:  14D07,  32G20
Keywords: Teichmüller curves, cyclotomic field, Neron model
@article{AIF_2008__58_1_63_0,
     author = {M\"oller, Martin},
     title = {Finiteness results for Teichm\"uller curves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {1},
     year = {2008},
     pages = {63-83},
     doi = {10.5802/aif.2344},
     mrnumber = {2401216},
     zbl = {1140.14010},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2008__58_1_63_0}
}
Möller, Martin. Finiteness results for Teichmüller curves. Annales de l'Institut Fourier, Volume 58 (2008) no. 1, pp. 63-83. doi : 10.5802/aif.2344. http://www.numdam.org/item/AIF_2008__58_1_63_0/

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