3 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…

The Dieudonné-module multiplicity conjecture. The multiplicity of $\mathbb E/\mathbb E(F^{2m+1}+V^{2m+1})$ in $D_m$ is $4^m$.

Let $\Bbbk$ be an algebraically closed field of characteristic $p>0$, and let $D$ be a $p$-divisible group over $\Bbbk$. Its isomorphism number $n_D$ is the smallest nonnegative in…