Algebraic Geometry Seminar
Higgs bundles on the Fargues-Fontaine curve
2025/12/22 (Mon.) 13:30~14:30
- Date : 2025/12/22 (Mon.) 13:30~14:30
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Ho Leung Fong
- Abstract :
Higgs bundles on algebraic varieties have many important applications, including the proof of the fundamental lemma and non-abelian Hodge theory. In this talk, I introduce a notion of Higgs bundles on the Fargues–Fontaine curve, a fundamental object in the local Langlands program that is not itself an algebraic variety. I will state a version of the BNR correspondence, which relates Higgs bundles with line bundles on suitable curves. I will then describe an action of a Picard stack on the moduli stack of Higgs bundles and show that, after taking the quotient by this action, the resulting stack factorises as a product of B_dR-affine Grassmannians. Finally, I will discuss connections with number-theoretic objects and outline several directions for future research.
