Properties
If
is a short exact sequence of G-modules, then we get the usual long exact sequence of Tate cohomology groups:
If A is an induced G module then all Tate cohomology groups of A vanish.
The zeroth Tate cohomology group of A is
- (Fixed points of G on A)/(Obvious fixed points of G acting on A)
where by the "obvious" fixed point we mean those of the form Σ g(a). In other words, the zeroth cohomology group in some sense describes the non-obvious fixed points of G acting on A.
The Tate cohomology groups are characterized by the three properties above.
Read more about this topic: Tate Cohomology Group
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