5 problems

Semistable comparison conjecture. For all $i\in \mathbb{Z}$ and $n\in \mathbb{Z}_{\ge 0}$, there is a natural isomorphism

Let $A$ be a discrete valuation ring with local parameter $\pi$, perfect residue field $k$ of characteristic $p>0$, and fraction field $K$ of characteristic zero. Let…

Let $k$ be a perfect field of characteristic $p>0$, and let $X$ be a smooth $d$-dimensional $k$-scheme. Write $X^{(a)}$ for the points of codimension $a$, $i_{*,x}$ for extension b…

Let $(A,d)$ be a perfect prism such that $A/d$ is $p$-torsion free, and let $S$ be a smooth $A/d$-algebra. Here $W_n\Omega_{S/(A/d)}^i$ denotes the degree-$i$ de Rham–Witt group, a…

Let $W_r\Omega^n_{\log}$ denote the logarithmic de Rham–Witt sheaf. Rational contractibility conjecture. Each logarithmic de Rham–Witt sheaf $W_r\Omega^n_{\log}$ is rationally cont…