3 problems

Fix a complete discretely valued field $K$ of mixed characteristic $(0,p)$, with ring of integers $\mathcal{O}_K$ and perfect residue field $k$, and let…

Variational Hodge conjecture. If $\alpha_b$ is the restriction of a class $\alpha\in{\operatorname{H}}^{2r}({\mathcal X}^{\operatorname{an}},{\mathbb Q})$, equivalently if it is in…

$p$-adic variational Hodge conjecture. For $Z_k\in{\mathscr Z}^r(X_k)_{\mathbb Q}$, if