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arxiv: 1709.00998 · v2 · pith:LQFOHMOHnew · submitted 2017-09-04 · 🧮 math.NT

Intersections of Class Fields

Lars K\"uhne This is my paper
classification 🧮 math.NT
keywords classfieldspointsrestrictionabelianadditionalgebraicandr
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Using class field theory, we prove a restriction on the intersection of the maximal abelian extensions associated with different number fields. This restriction is then used to improve a result of Rosen and Silverman about the linear independence of Heegner points. In addition, it yields effective restrictions for the special points lying on an algebraic subvariety in a product of modular curves. The latter application is related to the Andr\'e-Oort conjecture.

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  1. Independence of CM points in Elliptic Curves

    math.NT 2019-07 unverdicted novelty 6.0

    Theorem classifying all linear dependencies among n images of CM points in elliptic curves under parameterizations from modular or Shimura curves.