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, Rational points of abelian varieties with values in towers of number fields, Invent
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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.