Letter to Deligne 28.03.90
Concerning the signs in the theory of Shimura varieties.
scanned 180KB
MR review of Shimura: Collected Papers
With footnotes, not part of the review sent to MR.
22.12.03.
22.02.04. Added more footnotes pdf
Canonical models of Shimura curves
As an introduction to Shimura varieties, and, in particular, to Deligne's
Bourbaki and Corvallis talks, I explain the main ideas and results of the
general theory of Shimura varieties in the context of Shimura curves.
16.09.02 (rough draft, called Canonical models for modular curves)
04.04.03
MR featured review of: Harris and Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties,
Annals of Math. Studies, Princeton UP, 2001.
(with endnotes not part of review sent to MR)
13.06.02 dvi, pdf
Thesis
This has been superseded by my 1968 papers in Inventiones Math.
pdf (5M)
Abelian Varieties with Complex Multiplication (for Pedestrians)
This is the text for an article that I wrote and disseminated in
September 1981, except that I've updated the references, corrected
a few misprints, and added a table of contents, some footnotes, and
an addendum.
The original article gave a simplified exposition of Deligne's
extension of the Main Theorem of Complex Multiplication to all
automorphisms of the complex numbers. The addendum discusses some
additional topics in the theory of complex multiplication.
dvi, pdf.
Kazhdan's Theorem on Arithmetic Varieties.
Define an arithmetic variety to be the quotient of a bounded symmetric
domain by an arithmetic group. An arithmetic variety is algebraic, and the
theorem in question states that when one applies an automorphism of the
field of complex numbers to the coefficients of an arithmetic variety the
resulting variety is again arithmetic.
This article simplifies Kazhdan's proof. In particular, it avoids recourse to the
classification theorems.
It was originally completed on March 28, 1984, and distributed in
handwritten form.
22.06.01 Put the complete manuscript on the web.
12.07.01 Fixed about 30 misprints. dvi pdf
Talks at IAS on Shimura varieties
The notes for 4 lectures I gave at IAS in early 1995 giving an introduction to Shimura varieties, and discussing the problems that arise in the attempt to understand their zeta functions.
dvi, pdf.
The (failure of the) Hasse principle for centres of semisimple groups
Proves that the Hasse principle holds for the centres of some semisimple groups over number fields, and fails for others.
The manuscript is dated 6th June, 1987.
11.12.2003: ps, pdf.