## Some modular abelian surfaces

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Frank Calegari, Shiva Chidambaram and Alexandru Ghitza
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## Abstract:

In this note, we use the main theorem of Boxer, Calegari, Gee, and Pilloni in*Abelian surfaces over totally real fields are potentially modular*( arXiv:1812.09269, 2018) to give explicit examples of modular abelian surfacesÂ $A$ withÂ $\operatorname {End}_{\mathbf {C}} A = \mathbf {Z}$ andÂ $A$ smooth outsideÂ $2$, $3$, $5$, andÂ $7$.

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## Additional Information

**Frank Calegari**- Affiliation: Department of Mathematics, The University of Chicago, 5734 S University Avenue, Chicago, Illinois 60637; and School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia
- MR Author ID: 678536
- Email: fcale@math.uchicago.edu
**Shiva Chidambaram**- Affiliation: Department of Mathematics, The University of Chicago, 5734 S University Avenue, Chicago, Illinois 60637
- Email: shivac@uchicago.edu
**Alexandru Ghitza**- Affiliation: School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia
- MR Author ID: 713726
- Email: aghitza@alum.mit.edu
- Received by editor(s): November 4, 2018
- Received by editor(s) in revised form: February 5, 2019
- Published electronically: April 1, 2019
- Additional Notes: The first author was supported in part by NSF Grant DMS-1701703.
- © Copyright 2019 American Mathematical Society
- Journal: Math. Comp.
**89**(2020), 387-394 - MSC (2010): Primary 11G10, 11F46; Secondary 11Y40, 11F80
- DOI: https://doi.org/10.1090/mcom/3434
- MathSciNet review: 4011548