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Let $A/S$ be an abelian scheme over a scheme S of characteristic p. I would like to know if it is possible to recover $A/S$ (up to isogeny) from its $p$-divisible group $A[p^\infty]/S$.

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    $\begingroup$ It seems to me that you need to put more hyoothesis on $S$ in order to have some chance to have the result, like being of finite type over a finite field... For example, if $S$ is the spectrum of an algebraically closed field, I guess the result is false... $\endgroup$
    – Xarles
    Aug 30, 2012 at 12:07

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