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In the development of local class field theory, a very fundamental theorem is that, for every local field $K$ of characteristic zero, $H^2(K, \mu) \cong \mathbb{Q}/\mathbb{Z}$. $(*)$ Neukirch et al. ...

It is well-known from local class field theory that the Brauer group $\text{Br}(k)$ of a local field $k$ gets killed as you pass to sufficiently large extensions of $k$. In particular, $\text{Br}(L)(p)...

In local class field theory, the reciprocity map is constructed by using the isomorphism ${\rm Br}(F)\simeq \mathbb{Q/Z}$, where $F$ is a local field and ${\rm Br}(F)$ is its Brauer group. The ...