Periods of Hecke characters. (English) Zbl 0659.14001

Lecture Notes in Mathematics, 1301. Berlin etc.: Springer-Verlag. XV, 160 p.; DM 28.50 (1988).
The present article is devoted to the motivic theory for several objects around the periods of Hecke characters.
The objects are Shimura-Taniyama’s theorem for complex multiplication (I,§ 1) absolute Hodge cycles (I,§ 2), Hecke characters (I,§§ 3-5), Taniyama group (I,§ 6), Jacobi sum (I,§ 7), Chowla-Selberg formula (III) and modular forms (V).
The Chapter II is the technical heart of this article. Chapter IV mainly concerns with Shimura’s relations between periods of abelian varieties of CM type and generalizations of the Chowla-Selberg formula to abelian fields from the view point of motifs.
Reviewer: K.Katayama


14A20 Generalizations (algebraic spaces, stacks)
14G25 Global ground fields in algebraic geometry
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
14K22 Complex multiplication and abelian varieties
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