Torsors, Étale Homotopy and Applications to Rational Points

Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.

List of contributors; Preface; Part I. Lecture Notes: 1. Three lectures on Cox rings Jürgen Hausen; 2. A very brief introduction to étale homotopy Tomer M. Schlank and Alexei N. Skorobogatov; 3. Torsors and representation theory of reductive groups Vera Serganova; Part II. Contributed Papers: 4. Torsors over luna strata Ivan V. Arzhantsev; 5. Abélianisation des espaces homogènes et applications arithmétiques Cyril Demarche; 6. Gaussian rational points on a singular cubic surface Ulrich Derenthal and Felix Janda; 7. Actions algébriques de groupes arithmétiques Philippe Gille and Laurent Moret-Bailly; 8. Descent theory for open varieties David Harari and Alexei N. Skorobogatov; 9. Factorially graded rings of complexity one Jürgen Hausen and Elaine Herppich; 10. Nef and semiample divisors on rational surfaces Antonio Laface and Damiano Testa; 11. Example of a transcendental 3-torsion Brauer-Manin obstruction on a diagonal quartic surface Thomas Preu; 12. Homotopy obstructions to rational points Yonatan Harpaz and Tomer M. Schlank.