Let $V$ be a projective variety (possibly reducible) in $\mathbb{P}^n$ defined over $\mathbb{Z}$.
What is the relation between the degree of $V$ seen as a variety over $\overline{\mathbb{Q}}$ and the degree of $V$ seen as a variety over ${\overline{\mathbb{F}}_p}$ for a prime $p$?
It seems that the degree could fall at some primes, probably finitely many. If true, I would be grateful for a reference of this.