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p-Adic Methods in Arithmetic Geometry

Title
p-Adic Methods in Arithmetic Geometry
Funding
ARC | Discovery Projects
Contract (GA) number
DP0453134
Start Date
2004/01/01
End Date
2006/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0453134

 

  • Canonical coordinates on the canonical lift

    In this article we prove the existence of a canonical theta structure for the canonical lift of an ordinary abelian variety.

    Higher dimensional 3-adic CM construction

    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 ...
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