Infinite multiplicity of roots of unity of the Galois group in the representation on elliptic curves |
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Authors: | Bo-Hae Im |
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Institution: | Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA |
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Abstract: | Let K be a number field, an algebraic closure of K and E/K an elliptic curve defined over K. Let GK be the absolute Galois group of over K. This paper proves that there is a subset Σ⊆GK of Haar measure 1 such that for every σ∈Σ, the spectrum of σ in the natural representation of GK 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 of GK. |
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Keywords: | primary 11G05 |
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