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arXiv · 2504.21125

Compact approximation and descent for algebraic stacks

Jack Hall·Alicia Lamarche·Pat Lank·Fei Peng
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Abstract

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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Jack Hall, Alicia Lamarche, Pat Lank, Fei Peng. 2025-04-29. Compact approximation and descent for algebraic stacks. https://arxiv.org/abs/2504.21125

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