Seminar in Algebraic Geometry and Number Theory

Additional information: There will be a gentle preseminar from 10.00-10.30 in MVL14, aiming to make the seminar accessible to Masters and PhD students.

Abstract: Division polynomials were introduced as a tool for computing scalar multiplication of points on elliptic curves. However, when evaluated at a point on the curve, these polynomials are often not coprime. This has led to the study of their common valuations, known as the cancellation exponent. In this talk, we begin by outlining the strategy behind proving the existing explicit formula for the cancellation exponent due to Cheon and Hahn, then introducing the idea of net polynomials, a higher-dimensional analogue of division polynomials. By explaining the key differences between net polynomials and division polynomials, we will discuss the necessary modifications to Cheon and Hahn's proof strategy, which allows us to extend their formula to account for complex multiplication (CM) points on elliptic curves using net polynomials.