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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Some modular abelian surfaces
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by Frank Calegari, Shiva Chidambaram and Alexandru Ghitza HTML | PDF
Math. Comp. 89 (2020), 387-394 Request permission

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
  • 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