Higher-dimensional 3-adic CM construction

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
Type de document :
Article dans une revue
Journal of Algebra, Elsevier, 2008, 319 (3), pp.971-1006. 〈10.1016/j.jalgebra.2007.11.016〉
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Soumis le : mardi 12 mai 2009 - 10:17:20
Dernière modification le : jeudi 21 juin 2018 - 01:23:56

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



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