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Compact approximation and descent for algebraic stacks

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arxiv 2504.21125 v1 pith:CLTCG6II submitted 2025-04-29 math.AG

Jack Hall , Alicia Lamarche , Pat Lank , Fei Peng This is my paper · ORCID
classification math.AG
keywords algebraicapproximationstackscompactderivedgenerationresultalong
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This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are quasi-finite and flat. This generalizes a result of Lipman--Neeman for schemes and extends a related result known for algebraic spaces. We also study the behavior of generation under the derived pushforward and pullback of a morphism between algebraic stacks.

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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. Dualizing complexes and $t$-structures for algebraic stacks

    math.AG 2026-02 conditional novelty 6.0 of 10

    Separated tame Deligne–Mumford stacks of finite presentation over a field admit dualizing complexes; the advertised t-structure classification is absent from the body.

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