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Hugo Chapdelaine
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smooth connected affine scheme over Z has good reduction almost everywhere

Let $f(x_1,\ldots,x_n)\in\mathbf{Z}[x_1,\ldots,x_n]$ be a polynomial. Assume that the variety cut out by $f$ is smooth and connected (so irreducible) over $\overline{\mathbf{Q}}$. Where can I find a proof of the following classical result: for almost all primes $p$, $f\pmod{p}$ is a smooth $\mathbb{F}_p$-scheme.

Hugo Chapdelaine
  • 7.6k
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  • 28
  • 70