5 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

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

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

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…