The converse is false: see http://arxiv.org/pdf/math/0605326 for some examples of varieties over finite extensions of Q_p whose l-adic cohomology is unramified away from p and crystalline at l = p, but the variety does not have good reduction.

The converse is false. See the lecture notes by Chandan Singh Dalawat at http://arxiv.org/abs/math/0605326, which give some examples of varieties over finite extensions of $\mathbb{Q}_p$ whose $\ell$-adic cohomology is unramified for $\ell \ne p$ and crystalline at $\ell = p$, but the variety does not have good reduction.