Arithmetic of Abelian Varieties in Families

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

A workshop on "Arithmetic of abelian varieties in families" will be held at the Centre Interfacultaire Bernoulli (CIB) in Lausanne, Switzerland during November 12 - 16, 2012, taking advantage of the presence of researchers at the semester-long program on "Rational points and algebraic cycles" there during Fall 2012: see http://rational.epfl.ch/workshop2.php The main topics of the workshop will be the distribution of arithmetic quantities (e.g., Mordell-Weil groups, Selmer groups, and Shafarevich-Tate groups) associated to elliptic curves and higher-dimensional abelian varieties, and the related questions of existence of rational points on varieties fibered in genus 1 curves. The theme of the supported workshop is about the rational number solutions to structured polynomial equations, a topic that was of interest to the ancient Greeks but is still largely a mystery today. Recently several groups of researchers working independently have made progress on these questions using a variety of methods, studying the statistical behavior of families of equations all at once instead of trying to understand individual equations in isolation. The grant will enable the PIs to bring the key researchers and their ideas together, and to involve young researchers so that the new ideas are assimilated into the next generation.