5 problems

Let $K/{\mathbb Q}$ be a number field and let $X/K$ be a smooth, projective variety. A prime has Hodge-Witt reduction for $X$ when the reduction of $X$ at that prime is Hodge-Witt.…

Let $E$ be an elliptic curve over $\mathbb{Q}$, and for each prime $p$ of good reduction write … where $i_E(p)$ divides $e_E(p)$. Thus $i_E(p)$ is the index of the largest cyclic s…

Let $X$ be a smooth, projective variety in the class considered by Joshi, including abelian varieties, and write $\dim(X)$ for its dimension. A prime has non-Hodge-Witt reduction i…

Let $K/{\mathbb Q}$ be a number field and let $A/K$ be an abelian variety. Serre's ordinarity conjecture. The abelian variety $A$ has infinitely many primes of good ordinary reduct…

Let $K/{\mathbb Q}$ be a number field and let $X/K$ be a smooth, projective variety. Serre's ordinarity conjecture. The variety $X$ has ordinary reduction modulo infinitely many no…