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

该项目是对BL 395/3-1中算法部分的补充，其中研究了Burns和Flach在Tate动机情况下的等变Tamagawa数猜想（ETNC）。在这个新项目中，我们想考虑在q上定义的阿贝尔变量A的基变化的ETNC，这里ETNC是著名的Birch和Swinnerton-Dyer猜想的等变改进。更明确地说，ETNC描述了扭曲hasse - weil - l函数的主要项，根据与附加到a的动机相关的上同调数据。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.