# formal smoothness versus reductness [closed]

I have the following situation: $R,H$ schemes over a field $k$ which we can assume to be algebraically closed, with $H$ reduced, $Y\subset R\times \mathbb{P}_k^n$ an open subset, $p:Y\rightarrow R$ the restriction of the projection onto the first factor and $w: Y\rightarrow H$ a surjective formally smooth morphism. How can I show that $R$ is reduced? Thank you

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This question was also asked on MO, where I posted an answer. (As noted in the comments there, one needs to assume that $p$ is surjective.) – Matt E Mar 15 '11 at 16:33
Since this question was just asked and answered on MathOverflow, I have closed it ("off topic" isn't a great reason). (See mathoverflow.net/questions/58534/…) – Akhil Mathew Mar 15 '11 at 17:09

## closed as off topic by Akhil MathewMar 15 '11 at 17:08

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