D\'{e}vissage for generation in derived categories
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.
Cite
@article{arxiv.2401.13661,
title = {D\'{e}vissage for generation in derived categories},
author = {Souvik Dey and Pat Lank},
journal= {arXiv preprint arXiv:2401.13661},
year = {2025}
}
Comments
Current: Pre-final version, accepted to Proc. Amer. Math. Soc. Previous: Improvement to main results and exposition