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This is probably a very basic question, but I can't wrap my head around it.

Given a normal open subgroup $U$ of a profinite group $G$ and a $G$-Module $A$ we have the following equation in group cohomology: $$\operatorname{res}^G_U \circ \operatorname{cor}^U_G = N_{G/U}$$

This follows immediately from the double coset formula (see NSW: Cohomology of Number Fields p.49).

My problem is twofold:

  1. What does $N_{G/U}$ mean in this context? Is it induced by dimension shifting from the case $n=0$: $N_{G/U}: A^U \rightarrow A^G$?
    And if this interpretation is correct:

  2. Is the induced homomorphism $N_{G/U}$ in some way equivalent or equal to $\operatorname{cor}^U_G$ which in the case $n=0$ is the above norm?

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Does the book you mention here define what the notation means? Or does it appear there just as a reference? In that case does the book allude to a reference? Thanks. – awllower Dec 8 '12 at 14:40

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