Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1212.1294 |
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Inhaltsangabe:
- Let $N$ be an odd and squarefree positive integer divisible by at least two relative prime integers bigger or equal than 4. Our main theorem is an asymptotic formula solely in terms of $N$ for the stable arithmetic self-intersection number of the relative dualizing sheaf for modular curves $X_1(N)/ \mathbb{Q}$. From our main theorem we obtain an asymptotic formula for the stable Faltings height of the Jacobian $J_1(N) / \mathbb{Q}$ of $X_1(N)/ \mathbb{Q}$, and, for sufficiently large N, an effective version of Bogomolov's conjecture for $X_1(N) / \mathbb{Q}$.