Follow-up to Chandan Singh Dalawat's excellent answer:  smooth curves over $\mathbb{F}_p$ can always be lifted to over $\mathbb{Z}_p$.  But there are smooth projective surfaces over $\mathbb{Z}/p^n$ that cannot be lifted to $\mathbb{Z}_p$, see [Link](https://arxiv.org/abs/math/0411469) .