Topology of $\mathbb{G}_m$-actions and applications to the moduli of Higgs bundles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866908292237754368 |
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| author | Herrero, Andres Fernandez Zhang, Siqing |
| author_facet | Herrero, Andres Fernandez Zhang, Siqing |
| contents | We explain some results concerning the topology of varieties and stacks equipped with an action of the multiplicative group $\mathbb{G}_m$. We apply these techniques to the moduli of Higgs bundles. Our main application is to upgrade the cohomological Nonabelian Hodge Theorem in positive characteristic to an isomorphism of cohomology rings compatible with cup product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03275 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topology of $\mathbb{G}_m$-actions and applications to the moduli of Higgs bundles Herrero, Andres Fernandez Zhang, Siqing Algebraic Geometry We explain some results concerning the topology of varieties and stacks equipped with an action of the multiplicative group $\mathbb{G}_m$. We apply these techniques to the moduli of Higgs bundles. Our main application is to upgrade the cohomological Nonabelian Hodge Theorem in positive characteristic to an isomorphism of cohomology rings compatible with cup product. |
| title | Topology of $\mathbb{G}_m$-actions and applications to the moduli of Higgs bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.03275 |