5 problems

Let $X$ be a smooth space in the setting of the paper, and consider the projective maps … Let $M$ be a corresponding $Z$-projective differential crystal spectrum. Logarithmic cryst…

Kummer pro-étale extension conjecture. The construction developed in the section should extend to suitable Kummer pro-étale sites with logarithmic perfectoid subdomains forming a b…

Logarithmic Kummer Poincaré conjecture. The logarithmic versions of the strictly exact long exact sequences in the Poincaré lemma for the rigid-analytic situation should hold for t…

Pro-étale Poincaré conjecture. The construction in this section should extend to the pro-étale sites, giving two strictly exact long exact sequences of topological derived de Rham…

Let $K$ be the base field, and let $C$ be a connected smooth projective curve over $K$ of genus $g\geq 1$. In the diamantine setting, one expects a universal pro-étale perfectoid c…