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Mathematics > Algebraic Geometry
Title: Descent conditions for generation in derived categories
(Submitted on 16 Aug 2023 (v1), last revised 28 Mar 2024 (this version, v6))
Abstract: This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian $J\textrm{-}2$ 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.
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