Hello, everyone. I want to ask a question about abelian scheme.
If $X$ is a scheme, proper, finite type, over Dedekind scheme $S$ with a section $e$, and all the fiber are abelian varieties with the identity sections which induced by $e$, does there exists an group structure on $X$ with identity section is $e$? if not could you please show me a counter example?
Thank you very much.