Article ID Journal Published Year Pages File Type
4587953 Journal of Algebra 2008 36 Pages PDF
Abstract

We find equations for the higher-dimensional analogue of the modular curve X0(3) using Mumford's algebraic formalism of algebraic theta functions. As a consequence, we derive a method for the construction of genus 2 hyperelliptic curves over small degree number fields whose Jacobian has complex multiplication and good ordinary reduction at the prime 3. We prove the existence of a quasi-quadratic time algorithm for computing a canonical lift in characteristic 3 based on these equations, with a detailed description of our method in genus 1 and 2.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory