The Herbrand quotient: a ratio of cardinalities of two [Tate cohomology](Unsorted/group%20cohomology.md) groups. Key in proof of [Artin reciprocity](Unsorted/Artin%20symbol.md). ![](attachments/Pasted%20image%2020220126213527.png) ![](attachments/Pasted%20image%2020220126213557.png) ![](attachments/Pasted%20image%2020220126213613.png)