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Descending strong generation in algebraic geometry

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arxiv 2502.08629 v1 pith:CGDT3Q4J submitted 2025-02-12 math.AG math.AC

Timothy De Deyn , Pat Lank , Kabeer Manali Rahul This is my paper · ORCID
classification math.AGmath.AC
keywords generationstrongalgebraiccategorynoetherianstatementszariskialgebro-geometric
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We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications we show that strong generation for the singularity category of a Noetherian separated scheme is Zariski local and obtain a strong generation result for the bounded derived category of a Noetherian concentrated algebraic stacks with finite diagonal.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Perfect generation for regular algebraic stacks

    math.AG 2026-01 conditional novelty 8.0 of 10

    Every regular Noetherian algebraic stack with quasi-finite diagonal has its derived category generated by a single perfect complex.

  2. Frobenius generation for algebraic stacks

    math.AG 2025-12 conditional novelty 7.0 of 10

    For Noetherian concentrated F-finite algebraic stacks with quasi-finite separated diagonal, Frobenius pushforwards of perfect complexes classically generate the bounded derived category.

  3. Remarks on diagonal dimension for algebraic stacks

    math.AG 2026-05 unverdicted novelty 6.0 of 10

    For smooth, separated, quasi-DM stacks over a regular affine scheme, the diagonal dimension is bounded by a formula in dim R, dim U, and cd(Y); for varieties with mild singularities it is at most 2·dim X.

  4. Measuring birational derived splinters

    math.AG 2025-10 accept novelty 6.0 of 10

    The paper defines μ_bds, a level-based invariant of the derived category that measures the failure of a scheme to be a birational derived splinter.

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