The Equivariant Tamagawa Number Conjecture for the base change of an abelian variety

阿贝尔簇基变的等变玉川数猜想

• 批准号: 171229853
• 负责人: Professor Dr. Werner Bley
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/171229853?language=en
• 关键词: Equivariant; Tamagawa; Number; Conjecture; base

This project is a complement to the algorithmic part of BL 395/3-1 where the Equivariant Tamagawa Number Conjecture (ETNC) of Burns and Flach is studied in the case of Tate motives. In this new project we want to consider ETNC for the base change of an abelian variety A which is defined over Q. Here ETNC is an equivariant refinement of the famous Birch and Swinnerton-Dyer conjecture. More explicitly, ETNC describes the leading terms of twisted Hasse-Weil-L-functions in terms of cohomological data associated to the motive which is attached to A. The aim of the project is to derive explicit formulations of these equivariant conjectures which makes them amenable to numerical verifications and to develop and implement algorithms in order to provide numerical evidence.

该项目是BL 395/3-1算法部分的补充，其中Burns和Flach的等变玉川数猜想（ETNC）在Tate动机的情况下进行了研究。在这个新项目中，我们想考虑在Q上定义的阿贝尔簇A的基变化的ETNC。这里ETNC是著名的Birch和Swinnerton-Dyer猜想的等变精化。更明确地说，ETNC描述扭曲Hasse-Weil-L-函数的主导项的上同调数据与动机，这是附加到A。该项目的目的是推导出这些等变结构的显式公式，使它们能够进行数值验证，并开发和实施算法，以提供数值证据。