Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Root numbers, Selmer groups, and non-commutative Iwasawa theory

Authors: John Coates, Takako Fukaya, Kazuya Kato and Ramdorai Sujatha
Journal: J. Algebraic Geom. 19 (2010), 19-97
Published electronically: April 15, 2009
MathSciNet review: 2551757
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Abstract: Let $ E$ be an elliptic curve over a number field $ F$, and let $ F_\infty$ be a Galois extension of $ F$ whose Galois group $ G$ is a $ p$-adic Lie group. The aim of the present paper is to provide some evidence that, in accordance with the main conjectures of Iwasawa theory, there is a close connection between the action of the Selmer group of $ E$ over $ F_\infty$, and the global root numbers attached to the twists of the complex $ L$-function of $ E$ by Artin representations of $ G$.

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Additional Information

John Coates
Affiliation: DPMMS, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, England

Takako Fukaya
Affiliation: Keio University, Hiyoshi, Kohoku-ku, Yokohama, 223-8521, Japan

Kazuya Kato
Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

Ramdorai Sujatha
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

Received by editor(s): July 1, 2007
Received by editor(s) in revised form: October 24, 2007
Published electronically: April 15, 2009
Additional Notes: The second author gratefully acknowledges support from the JSPS Postdoctoral Fellowship for research abroad

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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