Let F be a number field, and let \(F^{{\text {cyc}}}\) be obtained by adjoining to F all the roots of unity. We show that as E ranges over all elliptic curves defined over \(F^{{\text {cyc}}}\) with complex multiplication, the torsion subgroups \(E(F^{{\text {cyc}}})\) are finite and uniformly bounded in size.

中文翻译：

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CM病例的无畸形扭转

令F为数字字段，并通过将F的所有根都与F相连来获得\（F ^ {{\ text {cyc}}} \\）。我们证明，当E遍及\（F ^ {{\ text {cyc}}}} \）上定义的所有椭圆曲线并具有复杂乘法时，扭转子组\（E（F ^ {{\ text {cyc}}}） \）是有限的并且大小一致。