Open conditions for infinite multiplicity eigenvalues on elliptic curves

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Let E be an elliptic curve defined over a number field K. We show that for each root of unity zeta, the set Sigma(zeta) of sigma is an element of Gal((K) over bar /K) such that zeta is an eigenvalue of infinite multiplicity for or acting on E((K) over bar) circle times C has non-empty interior. For the eigenvalue -1, we can show more: for any sigma in Gal((K) over bar /K), the multiplicity of the eigenvalue - 1 is either 0 or infinity. It follows that Sigma(-1) is open. (c) 2006 Elsevier Inc. All rights reserved
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2006-05
Language
English
Article Type
Article
Citation

JOURNAL OF ALGEBRA, v.299, no.2, pp.707 - 713

ISSN
0021-8693
DOI
10.1016/j.jalgebra.2006.02.011
URI
http://hdl.handle.net/10203/213021
Appears in Collection
MA-Journal Papers(저널논문)
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