Dévissage for generation in derived categories
Abstract
We study a form of dévissage 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.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 154
- Issue
- 3
- Pages
- 997–1006
- Publication date
- 16 January 2026
- Language
- EN