Rational points on varieties and obstructions

HHU Düsseldorf, Wintersemester 2026/27

Teacher: Jun.-Prof. Dr. Marta Pieropan

Lecture room: 25.31.HS.5M
Schedule: Thursdays at 12:30. See http://grk2240.uni-wuppertal.de/schedule_WS2627.html

Graduate course for the Research Training Group 2240.

Content
The principles of Diophantine Geometry are recorded in a series of theorems and conjectures, which clarify how the set of rational points on a projective variety is determined by the geometry of the variety and by the base field. Some principles, such as the Potential Density Conjecture, concern the distribution of points, other ones, such as the C1 Conjecture and Ax-Kochen's Theorem concern the existence of rational points. The course will introduce some of these principles and results. It will focus on local-global principles to existence and density of rational points, and on their obstructions. The concepts of Brauer-Severi varieties, Brauer groups, cohomological dimension, adeles, and torsors will be introduced along the way.

Literature
Colliot-Thélène and Skorobogatov, The Brauer-Grothendieck Group, Ergeb. Math. Grenzgeb. (3), 71, Springer, Cham, 2021. Link
Poonen, Rational points on varieties, Grad. Stud. Math., 186, American Mathematical Society, Providence, RI, 2017. Link
Skorobogatov, Torsors and rational points, Cambridge Tracts in Math., 144, Cambridge University Press, Cambridge, 2001. Link