Let $A$ be a ring and $G$ be an affine commutative FPPF group scheme over $A$. Can we embed $G$ into a smooth group scheme over $A$?

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    $\begingroup$ I believe that this is open. Here is a similar question: mathoverflow.net/questions/22078/… $\endgroup$ – Ben Wieland May 17 at 2:51
  • $\begingroup$ One positive result: Let $N$ be a finite flat group scheme over a noetherian scheme $S$. Locally for the Zariski topology on $S$, there exists a projective abelian scheme $A$ and an embedding of $N$ into $A$. Raynaud 1979. $\endgroup$ – anon May 19 at 14:09

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