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Some modular abelian surfaces


Authors: Frank Calegari, Shiva Chidambaram and Alexandru Ghitza
Journal: Math. Comp.
MSC (2010): Primary 11G10, 11F46; Secondary 11Y40, 11F80
DOI: https://doi.org/10.1090/mcom/3434
Published electronically: April 1, 2019
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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 surfaces $ A$ with  $ \operatorname {End}_{\mathbf {C}} A = \mathbf {Z}$ and $ A$ smooth outside $ 2$, $ 3$, $ 5$, and $ 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
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
Email: aghitza@alum.mit.edu

DOI: https://doi.org/10.1090/mcom/3434
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.
Article copyright: © Copyright 2019 American Mathematical Society