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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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Root numbers of abelian varieties
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by Maria Sabitova PDF
Trans. Amer. Math. Soc. 359 (2007), 4259-4284 Request permission

Abstract:

We generalize a theorem of D. Rohrlich concerning root numbers of elliptic curves over number fields. Our result applies to arbitrary abelian varieties. Namely, under certain conditions which naturally extend the conditions used by D. Rohrlich, we show that the root number $W(A,\tau )$ associated to an abelian variety $A$ over a number field $F$ and a complex finite-dimensional irreducible representation $\tau$ of $\operatorname {Gal}(\overline {F}/F)$ with real-valued character is equal to $1$. We also show that our result is consistent with a refined version of the conjecture of Birch and Swinnerton-Dyer.
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Additional Information
  • Maria Sabitova
  • Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
  • Address at time of publication: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
  • MR Author ID: 707297
  • Email: sabitova@math.upenn.edu, sabitova@math.uiuc.edu
  • Received by editor(s): May 6, 2005
  • Received by editor(s) in revised form: July 21, 2005
  • Published electronically: April 11, 2007
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 4259-4284
  • MSC (2000): Primary 11G10; Secondary 11F80, 11G40, 11R32
  • DOI: https://doi.org/10.1090/S0002-9947-07-04148-7
  • MathSciNet review: 2309184