## On the grössencharacter of an abelian variety in a parametrized family

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- by Robert S. Rumely PDF
- Trans. Amer. Math. Soc.
**276**(1983), 213-233 Request permission

## 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.## References

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## Additional Information

- © Copyright 1983 American Mathematical Society
- 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