# 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

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topMöller, 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 -

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