Let $R$ be a finitely generated ring, that is, a $\mathbb{Z}$-algebra of finite type. Assume that $\operatorname{char}(R) = 0$. It follows from Noether's normalization lemma that $R$ can be embedded in the ring of integers $\mathcal{O}_K$ of a $p$-adic field $K$ for all but finitely many primes $p$.

(1) Is there a prime $p$ such that $R$ be embedded in $\mathcal{O}_K$ where $K/\mathbb{Q}_p$ is unramified? (2) If so, are there infinitely many such primes p?