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Transactions of the American Mathematical Society

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



Root numbers of abelian varieties

Author: Maria Sabitova
Journal: Trans. Amer. Math. Soc. 359 (2007), 4259-4284
MSC (2000): Primary 11G10; Secondary 11F80, 11G40, 11R32
Published electronically: April 11, 2007
MathSciNet review: 2309184
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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

Keywords: Abelian variety, root number, Weil-Deligne group.
Received by editor(s): May 6, 2005
Received by editor(s) in revised form: July 21, 2005
Published electronically: April 11, 2007
Article copyright: © Copyright 2007 American Mathematical Society