7 problems

Converse weight-bound conjecture. If, for all $l$, the weights of $H^l\otimes\mathbb{Q}(M)$ lie between $l+a$ and $l+b$, then

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…

Relative weight-detection conjectures. The conjecture $WD^n(X)$ holds if

Weight-detection conjecture. For every $r,n\ge 0$, if

Functor-category conjecture. The category $\underline{H}_{t_{hom}}(S)$ is equivalent to the category of those contravariant additive functors…

Let $(\underline{C},w)$ be a triangulated category with a weight structure, let $N\geq 0$, and write $\underline{C}^{[0,N]}$ for the corresponding weight range. The strong weight c…

Let $(\underline{C},w)$ be a triangulated category with a weight structure $w$, let $\underline{Hw}=\underline{C}^{w=0}$ be its heart, and let…