Higher dimensional 3-adic CM construction
| dc.creator | Carls, R. | |
| dc.creator | Kohel, D. | |
| dc.creator | Lubicz, D. | |
| dc.date | 2006-07-24 | |
| dc.date | 2007-09-01 | |
| dc.date.accessioned | 2026-07-07T08:54:41Z | |
| dc.date.available | 2026-07-07T08:54:41Z | |
| dc.description | We find equations for the higher dimensional analogue of the modular curve X_0(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. | |
| dc.description | 23 pages; major review | |
| dc.identifier | https://arxiv.org/abs/math/0607583 | |
| dc.identifier | http://arxiv.org/abs/math/0607583 | |
| dc.identifier | J. Algebra, Vol. 319 (2008), No. 3, p. 971-1006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146022 | |
| dc.subject | Number Theory | |
| dc.subject | 11G15, 11Y40, 14K25 | |
| dc.title | Higher dimensional 3-adic CM construction | |
| dc.type | text |