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arXiv · 2408.03275

Topology of $\mathbb{G}_m$-actions and applications to the moduli of Higgs bundles

Andres Fernandez Herrero·Siqing Zhang
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Abstract

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.

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Andres Fernandez Herrero, Siqing Zhang. 2024-08-06. Topology of $\mathbb{G}_m$-actions and applications to the moduli of Higgs bundles. https://arxiv.org/abs/2408.03275

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