Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Thursday, 16 June 2005, 16:00 - 17:00, lecture hall 401

Robert Carls (Sydney): Higher dimensional explicit CM theory.

Abstract:

We give equations satisfied by the canonical theta null point of a canonical lift over a 2-adic ring. Our equations are computed using Mumford's multiplication formula for algebraic theta functions. The canonical theta null point is defined in terms of the canonical theta structure. Solving our equations gives a method for computing class fields of CM fields similar to the one described in [GHKRW]. We demonstrate this by some examples. For proofs and more details see [C].

[C] Carls: Theta null points of canonical lifts I+II, preprint, download

[GHKRW] Gaudry, Houtmann, Kohel, Ritzenthaler, Weng: A p-adic CM-method for genus 2, preprint, download