6 problems

Let $X$ and $Y$ be smooth projective varieties, and let … be a splitting functor. A kernel functor is a functor represented by a kernel $K\in D^b\operatorname{Coh}(X\times Y)$. Ker…

Let $X_1$ and $X_2$ be smooth projective schemes over a field $\Bbbk$. An exact $\Bbbk$-linear functor … is Fourier–Mukai if there exists an object…

Injective-extension conjecture. The functor $\psi_\eta$ is continuous.

Lunts's conjecture. The functor $f$ is Fourier–Mukai.

Fourier–Mukai functor conjecture. All exact functors

A splitting functor is a functor between bounded derived categories of coherent sheaves on smooth projective varieties with the splitting properties defined by Kuznetsov. Kuznetsov…