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Acyclotomy of torsion in the CM case
The Ramanujan Journal ( IF 0.6 ) Pub Date : 2020-07-21 , DOI: 10.1007/s11139-020-00271-0
Michael Chou , Pete L. Clark , Marko Milosevic

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:

CM病例的无畸形扭转

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。

更新日期:2020-07-22
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