3 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 $X$ 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 $X$ be a smooth, projective Calabi–Yau threefold over a field of positive characteristic. Let $H^0(X,\Omega^1_X)$ denote its global one-forms and let $h^{1,2}_W$ be its $(1,2)$…