Common valuations of division polynomials - Naskręcki, Bartosz; Verzobio, Matteo; IST-BRIDGE: International postdoctoral program (Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2024)
In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.
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Rights: https://creativecommons.org/licenses/by/4.0/
Keywords: article; Elliptic curves -- Néron models -- division polynomials -- height functions -- discrete valuation rings