SPRING SCHOOL ON ABELIAN VARIETIES

Gerard van der Geer and Ben Moonen
University of Amsterdam
Korteweg-de Vries Institute for Mathematics
Plantage Muidergracht 24
1018 TV Amsterdam
The Netherlands

E-mail:    geer (GvdG)  or   bmoonen (BM), both at the domain   science . uva . nl

In May 2006 there will be a Spring School on Abelian Varieties. From Tuesday, 2 May 2006 until Wednesday, 24 May there will be courses on abelian varieties, aimed at advanced undergraduate students and graduate students. These courses will be given at the University of Utrecht. After a short break (25 May 2006 is Ascension Day), the Spring School will be concluded by a 3-day Workshop on Abelian Varieties, to be held at the University of Amsterdam.

The Spring School is organized by the Mathematics Research Institute (MRI) in the Netherlands, in collaboration with the Thomas Stieltjes Institute. For all general information about the Spring School we refer to the MRI webpage about the Spring School which also contains information about how to apply.

Especially for Dutch students, we note that in the Spring of 2006 there will be a Master's course on Abelian Varieties, which provides an excellent preparation for the Spring School. For further information, see the webpage of the Dutch Master Program in Mathematics.

• Ching-Li Chai: Monodromy of modular varieties

• Gunther Cornelissen: The Mordell-Weil Theorem for Abelian Varieties

• Bas Edixhoven: Moduli of Abelian Varieties

• Gerard van der Geer and Ben Moonen: Basic Theory of Abelian Varieties

• Frans Oort: Abelian Varieties over Finite Fields

• Marius van der Put: Complex Abelian Varieties

• Jozef Steenbrink: Jacobian Varieties

• Jaap Top: Rational Points over Finite Fields

Prerequisites. We expect students to have:

• some basic knowledge of algebraic geometry (varieties, morphisms, line bundles, divisors, differentials,...)
• familiarity with the basic notions in commutative algebra (groups, rings, fields, some Galois theory, modules, basic commutative algebra) and topology.

In some of the courses the language of sheaves and schemes shall be used. It is not strictly necessary to be already familiar with these notions, but we expect that, if necessary, students are willing to study parts of the theory by themselves, or to take a number of basic results for granted. Further it will be useful to have some familiarity with cohomology theory (cohomology of sheaves), though most of what is needed can also be accepted as a set of axioms.

Some familiarity with elliptic curves will certainly be helpful, but again this is not necessary.

Some references:

R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52. Familiarity with the material in Chapters 2 and 3 will give you a very good background for the Spring School, though certainly not all of it is needed.

Q. Liu, Algebraic Geometry and Arithmetic Curves. This is a more recent textbook on algebraic geometry using the language of schemes.

D. Mumford, Abelian Varieties.

C. Birkenhake and H. Lange, Complex Abelian Varieties. Grundlehren der mathematischen Wissenschaften 302. Springer.

D. Mumford, The red book of varieties and schemes.

A. Polishchuk, Abelian varieties, theta functions and the Fourier transform. Cambridge Tracts in Mathematics, 153. Cambridge University Press, Cambridge, 2003.

I.R. Shafarevich, Basic Algebraic Geometry.

M.F. Atiyah and I.G. MacDonald, Introduction to commutative algebra. Good and accessible textbook on commutative algebra.

M. Hindry and J.H. Silverman, Diophantine Geometry - an introduction. Graduate Texts in Mathematics 201.

J-P. Serre, Lectures on the Mordell-Weil Theorem. Aspects of Mathematics E15.

G. Cornell and J.H. Silverman, Arithmetic Geometry. Springer-Verlag, New York, 1986.

To the home page of Ben Moonen

Last modified: Tuesday, 25-Apr-2006 20:55:07 CEST