proof of Hilbert Theorem 90
Remember that two cocycles are called cohomologous, denoted by , if there exists , such that for all . Then
Now let be a cocycle. Then consider the map
since is a cocycle, i.e. . Then we get
Thus we have that is a 1-coboundary.
Now we prove the corollary. Denote the norm by . Now if , we have
where denotes the class of in . Since , is well defined. We have
Therefore is a cocycle. Because of Hilberts Theorem 90, there exists , such that .
|Title||proof of Hilbert Theorem 90|
|Date of creation||2013-03-22 15:19:27|
|Last modified on||2013-03-22 15:19:27|
|Last modified by||mathcam (2727)|