3 problems

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Positive-density conjecture for Hodge–Witt reduction
Let $K$ be a number field and let $X/K$ be a smooth projective variety. Say that $X$ has Hodge–Witt reduction at a prime of $K$ when its smooth reduction at that prime is Hodge–Wit…
Conjectureopenarithmetic-geometry hodge-witt number-fieldsarXiv posted 2 days ago
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Joshi's conjecture on Hodge-Witt symmetry under a mild hypothesis
Let $X$ be a smooth, proper variety over a perfect field of characteristic $p>0$ , and suppose that $X$ satisfies the fairly mild hypothesis referred to in the source as Conjecture.…
Conjectureopenhodge-witt positive-characteristic-geometryarXiv posted 2 days ago
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Hodge-Witt symmetry conjecture for liftable varieties
Hodge-Witt symmetry conjecture. The variety $X$ satisfies Hodge-Witt symmetry. In particular, Ekedahl's conditions hold:
Conjectureopenarithmetic-geometry crystalline-cohomology hodge-wittarXiv posted 2 days ago

Positive-density conjecture for Hodge–Witt reduction