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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3$\begingroup$ I believe that this is open. Here is a similar question: mathoverflow.net/questions/22078/… $\endgroup$– Ben WielandCommented May 17, 2019 at 2:51
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$\begingroup$ 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. $\endgroup$– anonCommented May 19, 2019 at 14:09
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