200405 VIGRE Number Theory Working Group
Organized by Brian Conrad and Chris Skinner
This year's topic is the theory of complex
multiplication for abelian varieties.
One goal is to produce a written account of
the complete proof of the Main Theorem
of Complex Multiplication using
the techniques of modern algebraic geometry,
and to determine the Lseries of a CM abelian variety in
terms of Hecke Lseries. We hope to also
treat some generalizations
as required in the theory
of Shimura varieties. As talks are TeXed up, they
will be listed with a link below.

Outline for the year:
pdf.
ps.

Main Theorem for CM elliptic curves:
pdf.

Analytic theory of abelian varieties:
pdf
ps.

Algebraic theory of abelian varieties:
pdf.

CM abelian varieties:
pdf.

Polarizations:
pdf.
ps.

HondaTate theory:
pdf.
ps.

The ShimuraTaniyama formula:
pdf.
ps.

Weil restriction and adelic points:
pdf.

Reflex norms:
pdf.
ps.

Serre's tensor construction:
pdf.
ps.

Main Theorem of complex multiplication:
pdf.
ps.

Lfunctions for CM abelian varieties:
dvi.
ps.

