Rational and integral points on higher dimensional varieties

December 11 to December 20, 2002

at the

American Institute of Mathematics, Palo Alto, California

organized by

Bjorn Poonen and Yuri Tschinkel

Original Announcement

This workshop will be devoted to the study of rational and integral points on algebraic varieties, primarily those of dimension at least two.

We are bringing together researchers in algebraic geometry, diophantine approximation, cohomological methods (e.g. the Brauer-Manin obstruction, universal torsors), analytic methods (e.g. the circle method), and algorithmic arithmetic geometry. We hope especially to facilitate communication between researchers studying theoretical aspects and those with a more computational bent.

The main questions to be addressed concern

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Lecture Notes:

  1. Colliot-Thelene 1: Rational points on surfaces with a pencil ...
  2. Colliot-Thelene 2: Rational points on surfaces with a pencil ...
  3. de Jong: Rationally Connected Varieties
  4. Graber: Rationally Connected Varieties
  5. Harari 1: Weak approximation on algebraic varieties (introduction)
  6. Harari 2: Weak approximation on algebraic varieties (cohomology)
  7. Hassett 1: Equations of Universal Torsors
  8. Hassett 2: Weak approximation for function fields
  9. Heath-Brown: Rational Points and Analytic Number Theory
  10. Mazur: Families of rationally connected subvarieties
  11. Peyre: Motivic height zeta functions
  12. Raskind: Descent on Simply Connected Algebraic Surfaces
  13. Rotger: Rational points on Shimura varieties
  14. Salberger: Arithmetic Bezout and Rational Points of Bounded Height
  15. Skorobogatov: Counterexamples to the Hasse Principle...
  16. Vojta: Big semistable vector bundles
  17. Wooley: The Circle Method
  18. Yafaev: Descent on certain Shimura curves
List of open problems
Miscellaneous Photos