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Dévissage for generation in derived categories (2401.13661v4)

Published 24 Jan 2024 in math.AG and math.AC

Abstract: This note is concerned with generation in the derived category of bounded complexes with coherent cohomology over a Noetherian scheme. We demonstrate a flavor of `d\'{e}vissage' by identifying two explicit collections of structure sheaves for closed subschemes that classically generate the bounded derived category. Amongst the two, one consists of those supported on the singular locus of the scheme. Moreover, building from the work of Aoki, we show the essential image of the derived pushforward along a proper surjective morphism of Noetherian schemes strongly generates the targets bounded derived category.

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