Common valuations of division polynomials
| Autor: | Naskręcki, Bartosz, Verzobio, Matteo |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/prm.2024.7 |
| Popis: | In this note we prove a formula for the cancellation exponent $k_{v,n}$ between division polynomials $\psi_n$ and $\phi_n$ associated with a sequence $\{nP\}_{n\in\mathbb{N}}$ of points on an elliptic curve $E$ defined over a discrete valuation field $K$. The formula is identical with the result of Yabuta-Voutier for the case of finite extension of $\mathbb{Q}_{p}$ and generalizes to the case of non-standard Kodaira types for non-perfect residue fields. Comment: Final version of the paper |
| Databáze: | arXiv |
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