Let us denote by $A$ the ring of integer-valued polynomials in $\mathbf{Q}[T]$.
We know that $A$ is not Noetherian and of dimension $2$. I would like to understand $A$ better, for instance
(a) what is the homological dimension of $A$?
(b) I think the fibre ring $A\otimes_{\mathbf{Z}} \mathbf{Z}/p$ should be related to the $p$-adic integers, can someone point out this connection?
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$A \otimes_{\mathbf{Z}} \mathbf{Z}/p$ is simply $A/p$. – Crostul Sep 06 '16 at 14:17
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Moreover, I suspect that $A/p \cong (\mathbf{Z}/p)^p$. – Crostul Sep 06 '16 at 14:34
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https://math.osu.edu/sites/math.osu.edu/files/steward_polynomials_2015.pdf Theorem 4.2 – David Gilbert Sep 06 '16 at 14:44