3 problems

Let $X$ be an affine smooth curve over $k$, and let $W$ denote the ring of Witt vectors of $k$. Write $X_1$ for the affine curve obtained by removing all but one of the points at i…

Non-Hodge-Witt reduction conjecture. There exist infinitely many primes $\mathfrak p$ of $K$ such that the domino associated to

The recurring-fantasy conjecture. For every nonzero $v\in H^1(X,W\mathcal O_X)$, the map $\langle v,-\rangle$ is injective, and for every nonzero $v'\in H^0(X,W\Omega^1_X)$, the ma…