Partial Hasse invariants for genus zero curves in Hilbert modular varieties
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912844272893952 |
|---|---|
| author | Bogo, Gabriele Li, Yingkun |
| author_facet | Bogo, Gabriele Li, Yingkun |
| contents | 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 Teichmüller 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partial Hasse invariants for genus zero curves in Hilbert modular varieties Bogo, Gabriele Li, Yingkun Number Theory Algebraic Geometry 11F03, 11F33, 11F41 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 Teichmüller 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. |
| title | Partial Hasse invariants for genus zero curves in Hilbert modular varieties |
| topic | Number Theory Algebraic Geometry 11F03, 11F33, 11F41 |
| url | https://arxiv.org/abs/2601.16929 |