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arXiv · 2606.06092

Higgs bundles on the Fargues-Fontaine curve

Ho Leung Fong
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Abstract

In this paper, we introduce a notion of Higgs bundles on the Fargues-Fontaine curve. We establish a version of the BNR correspondence, which relates Higgs bundles to line bundles on suitable curves. We then describe an action of a Picard stack on the moduli stack of Higgs bundles and show that, modulo this action, there is a natural injective map of \'etale-stacks from the product of $B_{dR}^+$-affine Springer fibers to the Hitchin fiber that induces an equivalence of categories on every geometric point. Finally, we discuss connections with number-theoretic objects.

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Ho Leung Fong. 2026-06-04. Higgs bundles on the Fargues-Fontaine curve. https://arxiv.org/abs/2606.06092

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