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Mathematics > Algebraic Geometry
Title: Descent conditions for generation in derived categories
(Submitted on 16 Aug 2023 (v1), revised 12 Sep 2023 (this version, v2), latest version 28 Mar 2024 (v6))
Abstract: This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian 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. Finally, it is demonstrated that the bounded derived category of a Noetherian scheme of finite type over a perfect field admits a strong generator, yielding new examples that may not necessarily be separated.
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