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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
4
votes
Specialization Map of family of abelian varieties
This is addressing the final question at the end of the edited version of the posted question, which finally gets to the heart of the matter (and without which the earlier parts of the question don't …
4
votes
Accepted
kernel of isogeny becomes constant after base change
Do you really mean to consider an abelian scheme over the entire ring of integers, and not just a localization thereof? Either way, every finite flat group scheme $G$ over a domain $R$ with fraction …