11 problems

Let $\mathcal{M}_{\textrm{loc}}$ be the category of localizing noncommutative spectral motives, in which non-connective $K$-theory is co-represented. Its objects arise from spectru…

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…

The thesis studies noncommutative motives and equivariant homotopy theory, including naive and genuine equivariant constructions. Noncommutative-motivic duality conjecture. This re…

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…

Let $k$ be the base field, let $\mathbf{SH}(k)_{\mathbb Q}$ denote the rational stable motivic homotopy category, and let $DM^{\mathcal{GW}}_{nc}(k)_{\mathbb Q}$ denote the rationa…

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

Let $k$ be a field of characteristic zero and let $\mathcal{A}$ be a smooth proper dg category. Define … … Here $\operatorname{NHom}(k)_\mathbb{Q}$ and…

Let $F$ be the coefficient field and let ${\mathcal A}$ be a smooth and proper dg category. Its $F$-linearized Grothendieck group $K_0({\mathcal A})_F$ carries homological equivale…

Noncommutative standard conjecture $C_{NC}({\mathcal A})$. The Künneth projectors are algebraic: they can be written as

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…