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The effective Shafarevich conjecture for abelian varieties of 
${\text {GL}_{2}}$-type
Part of:
Arithmetic algebraic geometry
Published online by Cambridge University Press: 19 May 2021
Abstract
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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.
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