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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 …
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4 votes
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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 …
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