Arithmetic of Abelian Varieties in Families

2012年11月12日至16日，将在瑞士洛桑伯努利学院间中心（CIB）举办一场关于“家庭中阿贝尔变量的算术”的研讨会，该研讨会利用了2012年秋季在那里进行的为期一学期的“有理点和代数循环”项目的研究人员。参见http://rational.epfl.ch/workshop2.phpThe研讨会的主要主题将是与椭圆曲线和高维阿贝尔变数相关的算术量的分布（例如，mordel - weil群，Selmer群和shafarevic - tate群），以及在1属曲线纤维的变数上存在有理点的相关问题。这次研讨会的主题是结构化多项式方程的有理数解，这是一个古希腊人感兴趣的话题，但在今天很大程度上仍然是一个谜。最近，几组独立工作的研究人员利用各种方法在这些问题上取得了进展，他们同时研究了方程族的统计行为，而不是试图孤立地理解单个方程。这笔拨款将使这些项目能够把关键研究人员和他们的想法聚集在一起，并让年轻研究人员参与进来，以便新想法被下一代吸收。

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.