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Open conditions for infinite multiplicity eigenvalues on elliptic curves
Bo-Hae Im, Michael Larsen
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…
Heegner points and Mordell-Weil groups of elliptic curves over large fields
Bo-Hae Im
Let $E/\bbq$ be an elliptic curve defined over $\bbq$ with conductor and $\gq$ the absolute Galois group of an algebraic closure $\bar{\bbq}$ of $\bbq$. We prove that for every…
Mordell-Weil groups and the rank of elliptic curves over large fields
Bo-Hae Im
Let be a number field, an algebraic closure of and an elliptic curve defined over . In this paper, we prove that if has a -rational point su…
Weak approximation for linear systems of quadrics
Bo-Hae Im, Michael Larsen
We give local conditions at the infinite places of a number field K ensuring that the intersection of n quadrics in projective N-space over K, N >> n, satisfies weak approximation.