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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.08747 |
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| _version_ | 1866915250505252864 |
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| author | Aranha, Dhyan Khan, Adeel A. Latyntsev, Alexei Park, Hyeonjun Ravi, Charanya |
| author_facet | Aranha, Dhyan Khan, Adeel A. Latyntsev, Alexei Park, Hyeonjun Ravi, Charanya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stacky concentration theorem Aranha, Dhyan Khan, Adeel A. Latyntsev, Alexei Park, Hyeonjun Ravi, Charanya Algebraic Geometry 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. |
| title | The stacky concentration theorem |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.08747 |