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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the existence of abelian surfaces with everywhere good reduction
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by Lassina Dembélé HTML | PDF
Math. Comp. 91 (2022), 1381-1403 Request permission


Let $D \le 2000$ be a positive discriminant such that $F = \mathbf {Q}(\sqrt {D})$ has narrow class number one, and $A/F$ an abelian surface of $\operatorname {GL}_2$-type with everywhere good reduction. Assuming that $A$ is modular, we show that $A$ is either a $\mathbf {Q}$-surface or is a base change from $\mathbf {Q}$ of an abelian surface $B$ such that $\operatorname {End}_\mathbf {Q}(B) = \mathbf {Z}$, except for $D = 353, 421, 1321, 1597$ and $1997$. In the latter case, we show that there are indeed abelian surfaces with everywhere good reduction over $F$ for $D = 353, 421$ and $1597$, which are non-isogenous to their Galois conjugates. These are the first known such examples.
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Additional Information
  • Lassina Dembélé
  • Affiliation: Department of Mathematics, University of Luxembourg, Esch-sur-Alzette L-4364, Luxembourg
  • ORCID: 0000-0001-9001-5035
  • Email:
  • Received by editor(s): April 5, 2020
  • Received by editor(s) in revised form: April 6, 2020, August 2, 2021, and August 15, 2021
  • Published electronically: December 3, 2021
  • Additional Notes: The author was supported by EPSRC Grants EP/J002658/1 and EP/L025302/1, a Simons Collaboration Grant (550029) and by the Luxembourg National Research Fund PRIDE/GPS/12246620
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 1381-1403
  • MSC (2020): Primary 11G10
  • DOI:
  • MathSciNet review: 4405499