5 problems

The Liu–Zheng construction assigns a six-functor formalism to the relevant geometric data. A morphism is truncated when it satisfies the truncation condition used in the constructi…

Gaitsgory–Rozenblyum's universality conjecture. The universal target for left $I$-adjointable functors is $\operatorname{Span}_{1\frac{1}{2}}(C,I)$, and dually the universal target…

Twisting classification conjecture. There is a canonical isomorphism of anima

Scholze's uniqueness conjecture. The six-functor formalisms produced by the Liu–Zheng construction are exactly those for which every morphism in $P$ is cohomologically proper and e…

Let $X$ be a complex scheme. The compact objects in the homotopy category … form a triangulated category, where $\mathcal{H}$ is the absolute Hodge spectrum and…