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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 213-233
  • MSC: Primary 14K22; Secondary 10D20, 10D25, 14K15, 14K25
  • DOI:
  • MathSciNet review: 684504