Workshop: Arithmetic of abelian varieties in families
12-16 November 2012, EPFL, Lausanne, Switzerland
OverviewThis workshop, held during the semester-long program "Rational points and algebraic cycles" at the CIB, will focus on the distribution of arithmetic quantities attached to abelian varieties, and on the related question of the existence of rational points on surfaces fibered into genus 1 curves over number fields.
- Enumeration of n-coverings of elliptic curves and abelian varieties, towards average sizes of Selmer groups
- Distribution of ranks, Selmer groups, and Shafarevich-Tate groups: models coming from linear algebra processes, heuristics à la Cohen-Lenstra, and proofs when possible
- Constructing abelian varieties with prescribed Selmer ranks by twisting
- Rational points on surfaces fibered in genus 1 curves
- Applications of the above to Hilbert's tenth problem and other undecidability problems
Invited speakersSpeakers include Manjul Bhargava, Mirela Ciperiani, Tim Dokchitser, Noam Elkies, Jordan Ellenberg, Wei Ho, Daniel Kane, Zev Klagsbrun, Ambrus Pal, Eric Rains, Karl Rubin, Alexandra Shlapentokh, Alice Silverberg, Nina Snaith, Michael Stoll, Jack Thorne, Olivier Wittenberg, and David Zureick-Brown.
Schedule and abstracts
Olivier Wittenberg (print version)