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arXiv · 2601.16929

Partial Hasse invariants for genus zero curves in Hilbert modular varieties

Gabriele Bogo·Yingkun Li
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Abstract

We construct characteristic-zero lifts of partial Hasse invariants for genus zero non-compact curves in Hilbert modular varieties. The construction is based on recent results on the associated Picard-Fuchs differential equations. As an application, we relate the size of the non-ordinary locus of the modulo $p$ reduction of these curves to the dimension of spaces of (twisted) modular forms. We compute it explicitly for several Teichm\"uller curves, obtaining Deuring-like formulae. Moreover, we study the modulo $p$ reduction of (twisted) modular forms on not necessarily arithmetic genus-zero Fuchsian groups with modular embedding.

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Gabriele Bogo, Yingkun Li. 2026-01-23. Partial Hasse invariants for genus zero curves in Hilbert modular varieties. https://arxiv.org/abs/2601.16929

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