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A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.

10 votes

Points of elliptic curves over cyclotomic extensions

Since you ask more generally for results on $E(\mathbb{Q}^{\mathrm{ab}})$, let me expand my comment into a short answer. Amoroso and Dvornicich discovered (A lower bound on the height in abelian ext …
Filippo Alberto Edoardo's user avatar