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arXiv · 2407.08747

The stacky concentration theorem

Dhyan Aranha·Adeel A. Khan·Alexei Latyntsev·Hyeonjun Park·Charanya Ravi
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Abstract

We give a sufficient criterion for the Chow or algebraic bordism groups of an algebraic stack, localized at a set of Chern classes of line bundles, to be concentrated in some closed substack. This is a vast generalization of the torus fixed-point localization theorem in equivariant intersection theory, which is the special case of the stack quotient of a scheme $X$ by an action of a torus $T$. Taking on the one hand an algebraic stack in place of $X$, we deduce a generalization of torus localization to algebraic stacks. Taking on the other hand any algebraic group $G$ instead of $T$, we obtain a localization theorem in $G$-equivariant intersection theory.

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Dhyan Aranha, Adeel A. Khan, Alexei Latyntsev, Hyeonjun Park, Charanya Ravi. 2025-04-21. The stacky concentration theorem. https://arxiv.org/abs/2407.08747

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