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.
Shlapentokh, Elliptic curves retaining their rank in finite extensions and Hilbert’s tenth problem for rings of algebraic numbers, Trans
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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.