8 problems

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…

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 $X$ be a regular scheme of finite type over $S$, with $S$ pure of characteristic $p>0$. Let $Sh_t(X/S)$ denote tame sheaves, let $i:Z\hookrightarrow X$ be the inclusion of a re…

Let $k$ be a perfect field of characteristic $p>0$, let $W(k)$ be its ring of Witt vectors, and let $X/k$ be a smooth variety. The overconvergent de Rham–Witt complex…

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…

Let $X$ be a smooth variety over a field of positive characteristic $p$, and let $n$ be a positive integer and $r$ and $i$ integers. Write $H^i_{{\mathrm M}}(X,\mathbf{Z}/p^n(r))$…