6 problems

L-infinity algebroid conjecture. There exists a minimal $L_{\infty}$-algebroid structure on $C_{Z/X}^{\vee}$ whose Chevalley–Eilenberg algebra is equivalent to…

Assume the setting of the derived blow-up $\mathbb{B}l_{Z/X}$ and let $pr_f:\mathbb{B}l_{Z/X}\to X$ be the relevant morphism. Let $\mathfrak{W}_{1-r,1-r}^{f}$ and…

Assume the setting of the derived blow-up $\mathbb{B}l_{Z/X}$ over $S$, with morphism $pr_{Z/X}:\mathbb{B}l_{Z/X}\to X$ and integer $r$ as in the main theorem. Let…

Assumption-free discrepancy and vanishing conjecture. The assumptions that $\mathbb{B}l_f$ is smooth and that $\pi_0(Y)-\pi_0(X)$ is nonempty can be removed from the discrepancy fo…

Derived blow-up filtration conjecture. There exist objects $D_l\in D^b_{\operatorname{coh}}(Y)$ for $-r-1\leq l\leq 0$ such that

Tor-amplitude conjecture. The cotangent complex $L_{\mathbb{B}l_f}$ has Tor-amplitude $[0,n]$.