Arithmetic of Abelian Varieties in Families

族中阿贝尔簇的算术

• 批准号: 1204946
• 负责人: Bjorn Poonen
• 金额: $ 4.6万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1204946&HistoricalAwards=false
• 关键词: Arithmetic; Abelian; Varieties; Families

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.

2012年11月12日至16日，将在瑞士洛桑的伯努利中心举办一次“阿贝尔族变种的算术”研讨会，利用2012年秋季在那里举行的为期一学期的“有理点和代数周期”项目的研究人员的存在：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族变种有关的算术量的分布(例如，莫德尔-韦尔群、塞尔默群和沙法雷维奇-塔特群)，以及在亏格1曲线上的簇上存在有理点的相关问题。支持的工作坊的主题是关于结构化多项式方程的有理数解，这是古希腊人感兴趣的话题，但在今天仍然是一个谜。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，他们同时研究了一系列方程的统计行为，而不是试图孤立地理解单个方程。这笔赠款将使私人投资促进机构能够将主要研究人员和他们的想法结合在一起，并让年轻研究人员参与进来，以便将新想法吸收到下一代中。