Descent conditions for generation in derived categories

Abstract

This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian $J\text{-}2$ scheme is preserved by the derived pushforward of a proper morphism. Consequently, we can produce upper bounds on the Rouquier dimension of the bounded derived category, and applications concerning affine varieties are studied. In the process, a necessary and sufficient constraint is observed for when a tensor-exact functor between rigidly compactly generated tensor triangulated categories preserves strong $\oplus$-generators.

Pre-final for publication

References in corpus (2)

• Desingularization of quasi-excellent schemes in characteristic zero
• Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties