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Algebraic number fields. (English) Zbl 0819.11044
Parshin, A. N. (ed.) et al., Number theory II: Algebraic number theory. Transl. from the Russian. Berlin: Springer-Verlag. Encycl. Math. Sci. 62, 1-269 (1992).
This survey of classical algebraic number theory, including class field theory, Galois theory of local and global fields, Iwasawa’s theory, $p$- adic $L$-functions and Fröhlich’s theory is a translation of the Russian edition [Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 62 (1990; Zbl 0722.11001)] with removed innumerous printing errors of the original. For the entire collection see [Zbl 0814.00007].

##### MSC:
 11Rxx Algebraic number theory: global fields 11-02 Research monographs (number theory) 11R23 Iwasawa theory 11R37 Class field theory for global fields 11R52 Quaternion and other division algebras: arithmetic, zeta functions 11R32 Galois theory for global fields 11R54 Other algebras and orders, and their zeta and $L$-functions 11R47 Other analytic theory 11R29 Class numbers, class groups, discriminants 11S31 Class field theory for local fields; $p$-adic formal groups 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations 20E18 Limits, profinite groups 11S20 Galois theory for local fields