Arithmetic of Abelian Varieties in Families

2012年11月12日至16日，将在瑞士洛桑的伯努利学院间中心（CIB）举办一个关于“家族中阿贝尔簇的算术”的研讨会，利用研究人员在2012年秋季期间参加为期一学期的“有理点和代数循环”项目的机会：见 http://rational.epfl.ch/workshop2.phpThe研讨会的主要主题将是算术量的分布（例如，Mordell-Weil群、塞尔默群和Shafarevich-Tate群）与椭圆曲线和高维交换簇，以及亏格1曲线中纤维簇上有理点存在的相关问题。支持的研讨会的主题是关于结构多项式方程的有理数解，这是古希腊人感兴趣的话题，但今天仍然是一个谜。最近，几组独立工作的研究人员使用各种方法在这些问题上取得了进展，一次性研究方程族的统计行为，而不是试图孤立地理解单个方程。 这项拨款将使研究所能够将主要研究人员及其想法汇集在一起，并使年轻研究人员参与进来，以便新的想法被下一代吸收。

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.phpThe 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.