Finiteness results for Teichmüller curves

Martin Möller[1]

  • [1] Universität Essen FB 6 (Mathematik) 45117 Essen (Germany)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 1, page 63-83
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Möller, Martin. "Finiteness results for Teichmüller curves." Annales de l’institut Fourier 58.1 (2008): 63-83. <http://eudml.org/doc/10317>.

@article{Möller2008,
abstract = {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.},
affiliation = {Universität Essen FB 6 (Mathematik) 45117 Essen (Germany)},
author = {Möller, Martin},
journal = {Annales de l’institut Fourier},
keywords = {Teichmüller curves; cyclotomic field; Neron model; cyclotomic fields; Neron models},
language = {eng},
number = {1},
pages = {63-83},
publisher = {Association des Annales de l’institut Fourier},
title = {Finiteness results for Teichmüller curves},
url = {http://eudml.org/doc/10317},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Möller, Martin
TI - Finiteness results for Teichmüller curves
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 1
SP - 63
EP - 83
AB - 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.
LA - eng
KW - Teichmüller curves; cyclotomic field; Neron model; cyclotomic fields; Neron models
UR - http://eudml.org/doc/10317
ER -

References

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