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Group cohomology
*October 9, 2009*

*Posted by Akhil Mathew in algebra.*

Tags: delta-functors, group cohomology, group homology

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Tags: delta-functors, group cohomology, group homology

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Group cohomology is a useful language for expressing the results of class field theory, among (many) other things. There are a few ways I could introduce this. I could define them as derived functors (i.e. as a special case of ) or satellites, which would be the most general, but I try to keep my posts somewhat self-contained. I could define them additionally as cochains or coboundaries. I’ve decided to give an axiomatic definition, which will include the previous ones. (more…)