## Duke Mathematical Journal

### Arithmetic Veech sublattices of $\operatorname{SL}(2,\mathbf{Z})$

#### Abstract

We prove that every algebraic curve $X/\overline{\mathbf{Q}}$ is birational over $\mathbf{C}$ to a Teichmüller curve. This result is a corollary of our main theorem, which asserts that most finite-index subgroups of $\operatorname{SL}(2, \mathbf{Z})$ are Veech groups.

#### Article information

Source
Duke Math. J., Volume 161, Number 3 (2012), 415-429.

Dates
First available in Project Euclid: 1 February 2012

https://projecteuclid.org/euclid.dmj/1328105285

Digital Object Identifier
doi:10.1215/00127094-1507412

Mathematical Reviews number (MathSciNet)
MR2180399

Zentralblatt MATH identifier
1244.32009

#### Citation

Ellenberg, Jordan S.; McReynolds, D. B. Arithmetic Veech sublattices of $\operatorname{SL}(2,\mathbf{Z})$. Duke Math. J. 161 (2012), no. 3, 415--429. doi:10.1215/00127094-1507412. https://projecteuclid.org/euclid.dmj/1328105285

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