Abstract
The fundamental results given in this chapter do not necessarily form a sequence of logical steps for a proof of class field theory, but are written and commented so as to be used. This is so true that, as we will see several times, a classical proof consists in deducing local class field theory from global class field theory, as was initiated by Hasse and Schmidt in 1930, and in particular to base some local computations on global arguments (a typical example being the global computation of a local Hilbert symbol in 7.5); however here, in the description of the results, we will go from local to global, which seems more natural.
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© 2003 Springer-Verlag Berlin Heidelberg
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Gras, G. (2003). Reciprocity Maps Existence Theorems. In: Class Field Theory. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11323-3_3
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DOI: https://doi.org/10.1007/978-3-662-11323-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07908-5
Online ISBN: 978-3-662-11323-3
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