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We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.
Let be an elliptic curve over , let be an imaginary quadratic field, and let be a -extension of . Given a set of primes of , containing the primes above , and the primes of bad reduction for , write for the maximal algebraic extension of which is unramified outside . This paper is devoted to the study of the structure of the cohomology groups for and of the -primary Selmer group Sel, viewed as discrete modules over the Iwasawa algebra of
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