# Embed FPPF group scheme into smooth one

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 $$A$$?

• I believe that this is open. Here is a similar question: mathoverflow.net/questions/22078/… – Ben Wieland May 17 at 2:51
• 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. – anon May 19 at 14:09