Rational and integral points on higher dimensional varieties

This web page highlights some of the conjectures and open problems concerning Rational and integral points on higher dimensional varieties.

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  1. 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
  2. Problems
    1. List of open problems
    2. Photos
  3. Glossary
  4. Miscellaneous Photos

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