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Rational points and algebraic cycles

1 July 2012 - 31 December 2012, EPFL, Lausanne, Switzerland

Overview

The study of rational solutions to polynomial equations is ancient, but recently there have been advances, thanks to ideas coming from unexpected directions within mathematics. This semester-long program at the CIB will study rational points on varieties, along with related problems in algebraic geometry over non-algebraically closed fields, in particular those concerning algebraic cycles.

Topics

We expect the following to be investigated during the course of the semester:

• Cohomological obstructions to rational points (e.g., Brauer-Manin obstruction, descent obstruction)
• Arithmetic applications of étale homotopy theory
• Nonabelian analogues of Chabauty's method
• Fundamental groups and anabelian conjectures
• Motivic conjectures
• Arithmetic aspects of Chow groups
• Diophantine subsets of rational points
• Variation of ranks and Selmer and Shafarevich-Tate groups in families of abelian varieties

Activities

All events take place at EPFL in Lausanne unless otherwise specified.

Workshops

• Cohomological methods in arithmetic geometry, September 10-14, 2012 at U. Zürich
• Arithmetic of abelian varieties in families, November 12-16, 2012 (register)

Minicourses

• Arithmetic applications of étale homotopy theory, by Yonatan Harpaz and Tomer Schlank, Mondays and Wednesdays from July 2 to August 29, 2012, during 14:00-14:45 and 15:15-16:00 each day (syllabus)
• Arithmetic of del Pezzo and K3 surfaces, by Anthony Várilly-Alvarado, Tuesdays from July 10 to August 21, during 9:30-10:30 and 11:00-12:00 each day
• The motivic fundamental group, by Marc Levine, October 1-5, 2012

Other

Weekly seminars to be announced

Organizing Committee

Hélène Esnault (U. Duisburg-Essen), Andrew Kresch (U. Zürich), Bjorn Poonen (MIT), Alexei Skorobogatov (Imperial College London).

If you are interested in participating, please contact the organizers.