Title: Nakai--Moishezon criterion for derived categories

Abstract: Let $L$ be a line bundle on a proper variety $X$. If $L$ is ample, then its tensor powers generate the derived category of $X$. It is natural to ask whether there is some kind of converse to this statement. I will explain a necessary and sufficient condition for the tensor powers of $L$ to generate the derived category of $X$, and use it to give interesting examples of non-ample line bundles which satisfy this condition. The answer looks strikingly similar to the classical Nakai--Moishezon criterion, and has applications to the problem of reconstructing a variety from its derived category. This is joint work with Daigo Ito.