Infinite multiplicity of roots of unity of the Galois group in the representation on elliptic curves

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Let K be a number field, (K) over bar an algebraic closure of K and E/K an elliptic curve defined over K. Let G(K) be the absolute Galois group Gal((K) over bar /K) of K over K. This paper proves that there is a subset Sigma subset of G(K) of Haar measure 1 such that for every sigma is an element of Sigma, the spectrum of a in the natural representation E((K) over bar) circle times C of G(K) consists of all roots of unity, each of infinite multiplicity. Also, this paper proves that any complex conjugation automorphism in GK has the eigenvalue -1 with infinite multiplicity in the representation space E((K) over bar) circle times C of G(K). (c) 2005 Elsevier Inc. All rights reserved
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2005-10
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.114, no.2, pp.312 - 323

ISSN
0022-314X
DOI
10.1016/j.jnt.2005.06.002
URI
http://hdl.handle.net/10203/212957
Appears in Collection
MA-Journal Papers(저널논문)
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