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
DOI: https://doi.org/10.1090/S1056-3911-09-00504-9
Published electronically: April 15, 2009
MathSciNet review: 2551757
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Abstract | References | Additional Information

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
Email: J.H.Coates@dpmms.cam.ac.uk

Takako Fukaya
Affiliation: Keio University, Hiyoshi, Kohoku-ku, Yokohama, 223-8521, Japan
Email: takakof@hc.cc.keio.ac.jp

Kazuya Kato
Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan
Email: kzkt@math.kyoto-u.ac.jp

Ramdorai Sujatha
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
Email: sujatha@math.tifr.res.in

DOI: https://doi.org/10.1090/S1056-3911-09-00504-9
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

American Mathematical Society