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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
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Contributor : Dominique Hervé Connect in order to contact the contributor
Submitted on : Tuesday, May 12, 2009 - 10:17:20 AM
Last modification on : Friday, February 5, 2021 - 3:39:06 AM

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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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