arXiv
Open Access
2023
Heights of Special Points on Quaternionic Shimura Varieties
Roy Zhao
Abstrak
Let $B/F$ be a quaternion algebra over a totally real number field. We give an explicit formula for heights of special points on the quaternionic Shimura variety associated with $B$ in terms of Faltings heights of CM abelian varieties. Special points correspond to CM fields $E$ and partial CM-types $φ\subset \mathrm{Hom}(E, \mathbb{C})$. We then show that our height is compatible with the canonical height of a partial CM-type defined by Pila, Shankar, and Tsimerman. This gives another proof that the height of a partial CM-type is bounded subpolynomially in terms of the discriminant of $E$.
Topik & Kata Kunci
Penulis (1)
R
Roy Zhao
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2023
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓