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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.
MSC:
11RxxAlgebraic number theory: global fields
11-02Research monographs (number theory)
11R23Iwasawa theory
11R37Class field theory for global fields
11R52Quaternion and other division algebras: arithmetic, zeta functions
11R32Galois theory for global fields
11R54Other algebras and orders, and their zeta and L-functions
11R47Other analytic theory
11R29Class numbers, class groups, discriminants
11S31Class field theory for local fields; p-adic formal groups
13F05Dedekind, Prüfer, Krull and Mori rings and their generalizations
20E18Limits, profinite groups
11S20Galois theory for local fields