Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587953 | Journal of Algebra | 2008 | 36 Pages |
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