DUALITY THEOREMS IN GALOIS COHOMOLOGY OVER NUMBER FIELDS
DUALITY THEOREMS IN GALOIS COHOMOLOGY OVER NUMBER FIELDS
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作者：
J. Tate
取在所有有限伽罗瓦扩张K上的直接极限，其中X的积分闭包Y在X上是非分歧的，这里GKJk表示这样一个扩张的伽罗瓦群，戈伊表示G中坐标在Y上的点的群。例如，如果X=k，我们的符号与[10]的符号一致。对于任何X，群H（X，C）是前有限群Gjr=lim GKlk（Spec X的基本群）的第r个上同调群，其中
the direct limit taken over all finite Galois extensions K of k in which the integral closure Y of X is unramified over X, where GKJk denotes the Galois group of such an extension, and where GY denotes the group of points of G with coordinates in Y. For example, if X=k, our notation coincides with that of [10]. For any X, the group H(X,C) is the r-th cohomology group of the profinite group Gjr=lim GKlk (fundamental group of Spec X) with