Geodesic
The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type
Forum of Mathematics, Sigma, Tome 9 (2021)

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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. 
@article{10_1017_fms_2021_29,
     author = {Rafael von K\"anel},
     title = {The effective {Shafarevich} conjecture for abelian varieties of ${\text {GL}_{2}}$-type},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2021.29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.29/}
}
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Rafael von Känel. The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.29

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