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The effective Shafarevich conjecture for abelian varieties of
${\text {GL}_{2}}$-type
Published online by Cambridge University Press: 19 May 2021
Abstract
In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of
${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov theory. Our result opens the way for the effective study of integral points on certain higher dimensional moduli schemes such as, for example, Hilbert modular varieties.
- Type
- Number Theory
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
References
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