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.

关于“科中阿贝尔簇算术”的研讨会将于 2012 年 11 月 12 日至 16 日在瑞士洛桑伯努利院际中心 (CIB) 举行，利用研究人员参加为期一个学期的“有理数算术”项目的机会。点和代数循环”，2012 年秋季：参见 http://rational.epfl.ch/workshop2.php 研讨会的主要主题是分布与椭圆曲线和高维阿贝尔簇相关的算术量（例如 Mordell-Weil 群、Selmer 群和 Shafarevich-Tate 群），以及在属 1 曲线中纤维化的簇上有理点存在性的相关问题。支持的研讨会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主题，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，同时研究方程组的统计行为，而不是试图孤立地理解单个方程。 这笔赠款将使 PI 能够将关键研究人员及其想法聚集在一起，并让年轻研究人员参与进来，以便新想法被下一代吸收。