6 problems

Let $X$ be a smooth projective scheme over a field, and let ${\mathbf D}^b_{\operatorname{Coh}}(X)$ denote its bounded derived category of coherent sheaves. An enhancement of this…

Let $X$ and $Y$ be smooth and projective schemes over a field. An exact functor … is a functor between bounded derived categories of coherent sheaves. Bernstein–Lunts–Lunts conject…

Uniqueness conjecture. The category $D^b\operatorname{Coh}(X)$ should have a unique enhancement.

Enhancement uniqueness conjecture. Then $\mathrm{T}$ admits a unique $\infty$-categorical enhancement.

Enhancement uniqueness conjecture. The homotopy category $h\mathcal{C}$ admits a unique $\infty$-categorical enhancement.

Enhancement uniqueness conjecture. Then