Intersection of class fields
Volume 198 / 2021
Acta Arithmetica 198 (2021), 109-127
MSC: Primary 11G18; Secondary 11R37, 11G05, 14G35.
DOI: 10.4064/aa180717-9-6
Published online: 18 January 2021
Abstract
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 André–Oort conjecture.
