The rank of elliptic curves over $Q^{ab}$ and the positive rank twists of elliptic curves


Bo-Hae Im

09:10:00 - 10:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

We prove that for an elliptic curve $E/K$ over a quadratic or cubic field $K$, the rank of elliptic curves over $KQ^{ab}$ is infinite and we show that for four elliptic curves $E_i/K$ for $i=1,2,3,4$, there is a finite extension $L$ of $K$ such that the rank $E_i^d(L)$ of each of twists is positive for infinitely many $d\in L^*/(L^*)^2$. A part of the results is a joint work with Prof. Larsen.

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