|
2004-05 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 L-series of a CM abelian variety in
terms of Hecke L-series. 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.
|
|
Honda-Tate theory:
pdf.
ps.
|
|
The Shimura-Taniyama 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.
|
|
L-functions for CM abelian varieties:
dvi.
ps.
|
|