Common valuations of division polynomials
Naskręcki B, Verzobio M. Common valuations of division polynomials. arXiv, 2203.02015.
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Author
Naskręcki, Bartosz;
Verzobio, MatteoISTA 
Abstract
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.
Publishing Year
Date Published
2022-03-03
Journal Title
arXiv
Article Number
2203.02015
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Cite this
Naskręcki B, Verzobio M. Common valuations of division polynomials. arXiv. doi:10.48550/arXiv.2203.02015
Naskręcki, B., & Verzobio, M. (n.d.). Common valuations of division polynomials. arXiv. https://doi.org/10.48550/arXiv.2203.02015
Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2203.02015.
B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” arXiv. .
Naskręcki B, Verzobio M. Common valuations of division polynomials. arXiv, 2203.02015.
Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” ArXiv, 2203.02015, doi:10.48550/arXiv.2203.02015.
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