Open Questions: Algebraic Geometry
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See also: Number theory 
Geometry and topology
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Math Forum Internet Mathematics Library: Algebraic Geometry
 Alphabetized list of links with extensive annotations.

Open Directory Project: Algebraic Geometry
 Categorized and annotated algebraic geometry links. A version of this
list is at
Google, with entries sorted in "page rank" order.

Algebraic Geometry
 A very good list of links, by
Tyler J. Jarvis.

Galaxy: Algebraic Geometry
 Categorized site directory. Entries usually include
descriptive annotations.
Sites with general resources
Surveys, overviews, tutorials

Algebraic geometry
 Article from
Wikipedia.

Rational and integral points on higher dimensional varieties
 An outline (literally) of some of the conjectures and open
problems in this area of arithmetic algebraic geometry. Part of the
Workshop Website Network of the
American Institute of Matheamtics.
Includes a detailed
glossary.

A sheaftheoretic refinement of the Tate conjecture
 Preprint of a technical paper by Bruno Kahn. DVI and PS
formats available.

Algebraic Geometry
 Course notes from an introductory course, available in DVI,
PS, and PDF formats. By J. S. Milne.

Lectures on Etale Cohomology
 Course notes from an introductory overview, available in DVI,
PS, and PDF formats. By J. S. Milne.

Abelian Varieties
 Course notes from an introduction to the geometry and the
arithmetic of abelian varieties available in DVI,
PS, and PDF formats. By J. S. Milne.
The Hodge conjecture

The Hodge Conjecture
 Brief description of the problem at the
Clay Mathematics Institute site by Pierre Deligne.
(A more complete description is available as a PDF file.)

Hodge conjecture
 Article from
Wikipedia.
 Arithmetic on Curves
Barry Mazur
Bulletin of the AMS, April 1986, pp. 207259
 Diophantine problems in number theory can usually be expressed
in terms of, or related to, arithmetic questions about algebraic
curves. Faltings' proof of Mordell's conjecture is a key result,
which deals with important concepts of algebraic geometry, such
as abelian varieties and jacobians.
 The Proof of the Mordell Conjecture
Spencer Bloch
The Mathematical Intelligencer, Vol. 6, No 2, 1984, pp. 4147
 Gerd Faltings's 1983 proof of the Mordell conjecture is one of
the most important accomplishments in the field of artithmetic
algebraic geometry. The proof also settled, as essential steps,
several other important questions as well, including conjectures
of John Tate and I. R. Shafarevich.
 Karen E. Smith; Lauri Kahanpää; Pekka Kekäläinen;
William Traves – An Invitation to Algebraic Geometry
SpringerVerlag, 2000
 Modern algebraic geometry is a notoriously difficult subject. It's
founded upon (and was often the motivation for) some of the most
abstract concepts of abstract algebra. But the authors do a fine
job, in a short book, of describing the basic principles of
the subject, some of the important developments of the last
100 years, and some of the most interesting open problems. And
the prerequisites are few – just a basic course in linear
algebra.
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