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arXiv · 2401.13661

D\'{e}vissage for generation in derived categories

Souvik Dey·Pat Lank
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Abstract

We study a form of d\'{e}vissage for generation in derived categories of Noetherian schemes. First, we extend a result of Takahashi from the affine context to the global setting, showing that the bounded derived category is classically generated by a perfect complex together with structure sheaves of closed subschemes supported on the singular locus. Second, we make an observation for how generation behaves under the derived pushforward of a proper surjective morphism between Noetherian schemes. These results enable us to explicitly identify strong generators for projective schemes with isolated singularities and for singular varieties over a perfect field.

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Souvik Dey, Pat Lank. 2024-01-24. D\'{e}vissage for generation in derived categories. https://arxiv.org/abs/2401.13661

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