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On the grössencharacter of an abelian variety in a parametrized family


Author: Robert S. Rumely
Journal: Trans. Amer. Math. Soc. 276 (1983), 213-233
MSC: Primary 14K22; Secondary 10D20, 10D25, 14K15, 14K25
DOI: https://doi.org/10.1090/S0002-9947-1983-0684504-7
MathSciNet review: 684504
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Abstract: We consider families of abelian varieties parametrized by classical theta-functions, and show that specifying the family and a CM point in Siegel space determines the grössencharacter of the corresponding CM abelian variety. We associate an adelic group to the family, and describe the kernel of the grössencharacter as the pull-back of the group under the map in Shimura's Reciprocity Law.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0684504-7
Keywords: Abelian variety, theta-function, complex multiplication, grössencharacter
Article copyright: © Copyright 1983 American Mathematical Society

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