The effective Shafarevich conjecture for abelian varieties of -type-Reference-Cited by-同舟云学术

The effective Shafarevich conjecture for abelian varieties of -type

Published:2021 Issue: Volume:9 Page:
ISSN:2050-5094
Container-title:Forum of Mathematics, Sigma
language:en
Short-container-title:Forum of Mathematics, Sigma

Author:

von Känel Rafael

Abstract

Abstract In this article we establish the effective Shafarevich conjecture for abelian varieties over

${\mathbb Q}$

${\text {GL}_2}$

-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.

Publisher

Cambridge University Press (CUP)

Subject

Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis

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