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Group cohomology October 9, 2009

Posted by Akhil Mathew in algebra.
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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 {\mathrm{Tor},\mathrm{Ext}}) 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…)