Rational and integral points on higher dimensional varieties

Original Announcement

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

• existence of points,
• distribution of points in various topologies, and
• distribution with respect to heights.

Material from the workshop

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