4 problems

Let $X$ be a variety over a field of characteristic $p>0$, let $W$ denote the ring of Witt vectors, and write $H^2_{\mathrm{crys}}(X/W)_{\mathrm{tor}}$ for the torsion part of its…

Superfluity conjecture. The condition

Geometric generic-rank conjecture. Lemma should remain valid with $B({\mathcal O}_{\overline{K}})$ replaced by $B({\overline{K}})$.

Let $S$ be the Fermat quartic surface, and consider the 20 lines on $S$ whose intersection form has determinant $-64$. Line-generation conjecture. These lines generate…