Open Conditions for Infinite Multiplicity Eigenvalues on Elliptic Curves
نویسنده
چکیده
Let E be an elliptic curve defined over a number field K. We show that for each root of unity ζ, the set Σζ of σ ∈ Gal(K/K) such that ζ is an eigenvalue of infinite multiplicity for σ acting on E(K)⊗ C has non-empty interior. For the eigenvalue −1, we can show more: for any σ in Gal(K/K), the multiplicity of the eigenvalue −1 is either 0 or ∞. It follows that Σ −1 is open.
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