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Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
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Is H^2(W_p,C^times) well-known?
It is known that $H^2(W, C^\times)$ is trivial, when $W$ is the Weil group of a global or local field, with the trivial action on $C^\times$, and the cohomology is taken in the sense of Moore (measura …