A generalisation of the Cassel-Tate pairing.
A generalisation of the Cassel-Tate pairing.
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卡塞尔-泰特配对的概括。
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
M. Flach
中科院分区：
文献类型：
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作者：
M. Flach
在最近的一篇论文[1]中，Bloch和Kato定义了一个群III(M)，它的动机在Q上，并在它的奇异上同调中格M。例如，如果动机是h(A)(L)，M是H(A(C)，2niI)，其中A是交换簇，则III(M)是对偶交换簇的TateShafarevich群，除以它的极大可除子群。III(M)的意义源于它与某一L值的猜想关系(见[1])，该猜想实际上是Birch和Swinnerton-Dyer猜想的广泛推广。一般说来，人们猜想III(M)是有限的，并且可以证明它对每个素数i有一个有限/-主分支。
In a recent paper [1] Bloch and Kato defmed a group III (M) for a motive over Q together with a lattice M in its singular cohomology. For example, if the motive is h (A) (l) and M is H(A(C),2niI) where A is an abelian variety, III(M) is the TateShafarevich group of the dual abelian variety, divided by its maximal divisible subgroup. The significance of III (M) derives from its conjectured relationship with a certain L-value (see [1]) which is in fact a vast generalisation of the conjecture of Birch and Swinnerton-Dyer. In general III (M) is conjectured to be fmite and one can prove that it has a finite /-primary component for each prime /.