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Preprint Number 2235
2235. Barry Mazur, Karl Rubin, and Alexandra Shlapentokh Existential definability and diophantine stability E-mail: Submission date: 21 August 2022 Abstract: Let K be a number field, let L be an algebraic (possibly infinite
degree)
extension of K, and let O_K ⊂ O_L be their rings of integers.
Suppose A is an abelian variety defined over K such that A(K) is
infinite
and A(L)/A(K) is a torsion group. If at least one of the following
conditions
is satisfied: Mathematics Subject Classification: 11U05 (Primary) 11G05, 11G10, 03D35 (Secondary) Keywords and phrases: |

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