Serre, Jean-Pierre Algebraic groups and class fields. Transl. of the French edition. (English) Zbl 0703.14001 Graduate Texts in Mathematics, 117. New York etc.: Springer-Verlag. ix, 207 p. DM 72.00 (1988). The author’s book “Groupes algébrique et corps de classes” was published first in 1959 (Paris; Zbl 0097.356). A second - corrected - edition thereof appeared in 1975 (cf. Zbl 0318.14004), enlarged with a bibliography which took into account the development of the theme up to that time. The volume under review is the English translation of this second edition. Cited in 5 ReviewsCited in 70 Documents MSC: 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11R37 Class field theory 14K30 Picard schemes, higher Jacobians 20G99 Linear algebraic groups and related topics 11S31 Class field theory; \(p\)-adic formal groups 14H40 Jacobians, Prym varieties Keywords:algebraic groups; class fields Citations:Zbl 0097.356; Zbl 0318.14004 PDF BibTeX XML Cite \textit{J.-P. Serre}, Algebraic groups and class fields. Transl. of the French edition. New York etc.: Springer-Verlag (1988; Zbl 0703.14001)