Tamagawa numbers for motives with (non-commutative) coefficients
Tamagawa numbers for motives with (non-commutative) coefficients
复制标题
具有（非交换）系数的动机的玉川数
作者：
D. Burns;M. Flach
设M是定义在数域上的动机，它允许有限维半简单q代数a的作用。我们给出并研究了M的a -等变l函数在0处的泰勒展开的导系数的一个猜想。该猜想同时推广和完善了Bloch、Kato、Fontaine、Perrin-Riou等人的Tamagawa数猜想，以及Fröhlich、Chinburg、M. Taylor等人提出的经典伽罗瓦模理论的中心猜想。我们猜想的精确表述取决于A中A阶的选择，对于A阶，M上存在一个“射影A结构”。如果a是极大阶，则保证这种结构的存在性，并且在许多a是非极大阶的自然例子中也存在这种结构。在每一个这样的情况下，关于非极大阶的猜想细化了关于极大阶的猜想。利用Deligne引入的虚对象范畴，提出了a中所有阶的行列式函子理论。2000数学学科分类：初级11G40；次级11R65 19A31 19B28
Let M be a motive which is defined over a number field and admits an action of a finite dimensional semisimple Q-algebra A. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at 0 of the A-equivariant L-function ofM . This conjecture simultaneously generalizes and refines the Tamagawa number conjecture of Bloch, Kato, Fontaine, Perrin-Riou et al. and also the central conjectures of classical Galois module theory as developed by Fröhlich, Chinburg, M. Taylor et al. The precise formulation of our conjecture depends upon the choice of an order A in A for which there exists a ‘projective A-structure’ on M . The existence of such a structure is guaranteed if A is a maximal order, and also occurs in many natural examples where A is non-maximal. In each such case the conjecture with respect to a non-maximal order refines the conjecture with respect to a maximal order. We develop a theory of determinant functors for all orders in A by making use of the category of virtual objects introduced by Deligne. 2000 Mathematics Subject Classification: Primary 11G40; Secondary 11R65 19A31 19B28