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

本项目是对《BL395/3-1》算法部分的补充，其中研究了Burns和Flach的等变Tamagawa数猜想(ETNC)在Tate动机的情况下。在这个新的项目中，我们要考虑定义在Q上的交换簇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用与A相关的动机的上同调数据来描述扭曲的Hasse-Weil-L函数的主要术语。该项目的目的是推导出这些等变猜想的显式公式，使它们适合于数值验证，并开发和实现算法以提供数值证据。

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.