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Timeline for Intuition for Group Cohomology

Current License: CC BY-SA 3.0

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Nov 14, 2012 at 2:28 comment added Filippo Alberto Edoardo I think this answer is really good. My point of view is that many things we care about in number theory are acted upon by Galois groups, and often "fixed elements come from below". Somethines, this is sadly false, like for ideals and ideal class group. Group cohomology is then very natural, because you have a tautological exact sequence defining the class group and you would like to compare objects in this sequence (which you care about genuinely because it is tautological) which are fixed by Galois with those coming from below.
Jun 7, 2011 at 23:32 history answered paul garrett CC BY-SA 3.0