5 problems

Let $G$ be a finite group. Let $_G\text{Top}$ denote the $\infty$-category of genuine left $G$-spaces, and let $\text{Top}^G$ denote the $\infty$-category of naive, or Borel, right…

Let $NcS^{\cdot-\cdot}$ be the category whose objects are dg-categories and whose morphisms are pairs of dg-functors $F,G$ equipped with a natural equivalence $F\simeq G$. Let…

Let $NcS$ be the category whose objects are dg-categories without additional structures, and let $\widetilde{NcS}(S)$ and $DM^{\mathcal{GW}}_{nc}(k)$ be the categories constructed…

Motivic Gersten's conjecture. For any commutative regular local ring $R$ and any integers $1\leq p\leq\dim R$, the inclusion functor…

Mamma conjecture. Given a group $G$, the fundamental additive invariant ${\nobreak\boldsymbol{\mathbf{E}}}^{\mathsf{fund}}$ has the ${\mathcal V}C$-assembly property when the base…