article published yes Bartosz Naskręcki author Matteo Verzobio author 7aa8f170-131e-11ed-88e1-a9efd01027cb0000-0002-0854-0306 TiBr department IST-BRIDGE: International postdoctoral program project 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. https://research-explorer.ista.ac.at/download/12311/20878/2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf application/pdfno Cambridge University Press2025 eng Elliptic curvesNéron modelsdivision polynomialsheight functionsdiscrete valuation rings 0308-2105 1473-7124 2203.02015 00117490710000110.1017/prm.2024.7 15551646-1660 B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5. Cambridge University Press, pp. 1646–1660, 2025. Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:<a href="https://doi.org/10.1017/prm.2024.7">10.1017/prm.2024.7</a>. Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2025. <a href="https://doi.org/10.1017/prm.2024.7">https://doi.org/10.1017/prm.2024.7</a>. Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. 2025;155(5):1646-1660. doi:<a href="https://doi.org/10.1017/prm.2024.7">10.1017/prm.2024.7</a> B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660. Naskręcki, B., &#38; Verzobio, M. (2025). Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press. <a href="https://doi.org/10.1017/prm.2024.7">https://doi.org/10.1017/prm.2024.7</a> Naskręcki B, Verzobio M. 2025. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 155(5), 1646–1660. 123112023-01-16T11:45:22Z2025-12-30T06:46:17Z