Remark 111.29.4. Let $h \in {\mathbf Z}[y]$ be a monic polynomial of degree $d$. Then:

The map $A = {\mathbf Z}[x] \to B ={\mathbf Z}[y]$, $x \mapsto h$ is finite locally free of rank $d$.

For all primes $p$ the map $A_ p = {\mathbf F}_ p[x]\to B_ p = {\mathbf F}_ p[y]$, $y \mapsto h(y) \bmod p$ is finite locally free of rank $d$.

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