Higher dimensional 3-adic CM construction

dc.creatorCarls, R.
dc.creatorKohel, D.
dc.creatorLubicz, D.
dc.date2006-07-24
dc.date2007-09-01
dc.date.accessioned2026-07-07T08:54:41Z
dc.date.available2026-07-07T08:54:41Z
dc.descriptionWe 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.description23 pages; major review
dc.identifierhttps://arxiv.org/abs/math/0607583
dc.identifierhttp://arxiv.org/abs/math/0607583
dc.identifierJ. Algebra, Vol. 319 (2008), No. 3, p. 971-1006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146022
dc.subjectNumber Theory
dc.subject11G15, 11Y40, 14K25
dc.titleHigher dimensional 3-adic CM construction
dc.typetext

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