Iwasawa-theoretic results for abelian varieties over Z_p^2-extensions are applied to Diophantine stability and used to refine the Mazur growth conjecture, with extension to the supersingular case.
Mazur, Modular curves and arithmetic
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On Iwasawa theory of abelian varieties over $\mathbb{Z}_p^2$-extension with applications to Diophantine stability and integally Diophantine extensions
Iwasawa-theoretic results for abelian varieties over Z_p^2-extensions are applied to Diophantine stability and used to refine the Mazur growth conjecture, with extension to the supersingular case.