3 problems

Let $X/{\mathbb C}$ be a smooth, proper variety, and consider primes of good reduction for $X$. A prime is an ordinary reduction prime if the reduction of $X$ is ordinary. Serre's…

Let $X$ be a smooth, irreducible $n$-dimensional projective variety defined over an algebraically closed field $k$ of characteristic zero. If $X_A$ is a model of $X$ defined over a…

Let $X$ be a smooth, connected, $n$-dimensional projective variety over an algebraically closed field $k$ of characteristic zero. Given a model of $X$ over a ${\mathbf Z}$-algebra…