Periods of Hecke characters / Norbert Schappacher
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1301Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1988ISBN: 9783540189152.ISSN: 1617-9692.Sujet MSC : 14A20, Foundations of algebraic geometry, Generalizations (algebraic spaces, stacks)14G25, Arithmetic problems in algebraic geometry. Diophantine geometry, Global ground fields
11F67, Discontinuous groups and automorphic forms, Special values of automorphic L-series, periods of modular forms, cohomology, modular symbols
11G15, Arithmetic algebraic geometry (Diophantine geometry), Complex multiplication and moduli of abelian varieties
14K22, Abelian varieties and schemes, Complex multiplication and abelian varietiesEn-ligne : Springerlink | Zentralblatt | MathSciNet
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. (Zentralblatt)
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