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Open conditions for infinite multiplicity eigenvalues on elliptic curves

Bo-Hae Im·Michael Larsen
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Abstract

Let E be an elliptic curve defined over a number field K, V the complexification of the group of rational points of E over an algebraic closure L of K, and G the Galois group Gal(L/K). We show that for each root of unity w, the set of elements g in G such that w is an eigenvalue of infinite multiplicity for g acting on V has non-empty interior.

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Bo-Hae Im, Michael Larsen. 2006-02-04. Open conditions for infinite multiplicity eigenvalues on elliptic curves. https://arxiv.org/abs/math/0503156

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