It is well known that every local field (i.e. nondiscrete topological field locally compact with respect to the topology) is the completion of some global field. I know the argument, a nice exposition is 


<http://math.stanford.edu/~conrad/248APage/handouts/localglobal.pdf>


My question is, does anyone know a *published* reference for this fact? 



Reference for: Every local field can be realized as the completion of a global field
F. Lorenz: *[Algebra. Volume II: Fields with Structure, Algebras and Advanced Topics](http://www.springer.com/jp/book/9780387724874)*, Theorem 2 p. 78.


