Journal of Algebraic Geometry

Author(s): John Coates; Takako Fukaya; Kazuya Kato; Ramdorai Sujatha
Journal: J. Algebraic Geom. 19 (2010), 19-97.
Posted: April 15, 2009
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Abstract: Let

be an elliptic curve over a number field

, and let $F_\infty$ be a Galois extension of

whose Galois group

is a

-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

over $F_\infty$ , and the global root numbers attached to the twists of the complex

-function of

by Artin representations of

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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

PII: S 1056-3911(09)00504-9
Received by editor(s): July 1, 2007
Received by editor(s) in revised form: October 24, 2007
Posted: April 15, 2009
Additional Notes: The second author gratefully acknowledges support from the JSPS Postdoctoral Fellowship for research abroad

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