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Article Dans Une Revue Journal of Algebra Année : 2008

Higher-dimensional 3-adic CM construction

Résumé

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

Dates et versions

hal-00383119 , version 1 (12-05-2009)

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Robert Carls, David Kohel, David Lubicz. Higher-dimensional 3-adic CM construction. Journal of Algebra, 2008, 319 (3), pp.971-1006. ⟨10.1016/j.jalgebra.2007.11.016⟩. ⟨hal-00383119⟩
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