arXiv subjects

Ho Leung Fong

Publications and source records attributed to Ho Leung Fong.

3 recordsLinked to original sources

arXiv2026

Adjoint $L$-functions, congruence ideals, and Selmer groups over $\mathrm{GL}_n$

In this paper, we relate $L(1,π,\mathrm{Ad}^\circ)$ to the congruence ideals for cohomological cuspidal automorphic representations $π$ of $\mathrm{GL}_n$ over any number field. We then use this result to deduce relationships between the congruences of automorphic forms and adjoint $L$-functions. For CM and totally real fields, we apply the result to obtain a lower bound on the cardinality of certain Selmer groups in terms of $L(1,π,\mathrm{Ad}^\circ)$.

math.NT↗

arXiv2026

Higgs bundles on the Fargues-Fontaine curve

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 étale-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.

math.AG↗

arXiv2021

On Chow stability and balanced embeddings

An important result of Zhang states that for a projective variety, the existence of a balanced embedding is equivalent to Chow stability. In this paper, we shall prove that Chow stability implies that a balanced embedding exists via the continuity method. Our proof is conditional on a technical hypothesis about restrictions of Hamiltonians to subschemes of projective space.

math.AG↗