Dualizability of derived categories of algebraic stacks

2025/09/17 by Germán Stefanich, Stefanich, Germán · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2509.14231

Abstract

We show that, for a Noetherian algebraic stack with quasi-affine diagonal X, the stable ∞-category of quasi-coherent sheaves on X is dualizable if and only if the reduced identity component of the stabilizer of X at every geometric point of positive characteristic is a torus. Along the way, we show that this condition on stabilizers is also equivalent to an array of other categorical conditions of interest.

Citations

• Descendability of Faithfully Flat Covers of Perfect Stacks
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• Non-left-complete derived categories
• The resolution property for schemes and stacks
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Cited by

• Geometric Categories for Continuous Gauging

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• Equivalences of derived categories of sheaves on tame stacks
• Derived categories of coherent sheaves
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• Stability conditions on affine Noetherian schemes
• The stable derived category of a noetherian scheme