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Journal Article

Intersections of class fields

MPS-Authors
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Kühne,  Lars
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

1709.00998.pdf
(Preprint), 253KB

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Citation

Kühne, L. (2021). Intersections of class fields. Acta Arithmetica, 198(2), 109-127. doi:10.4064/aa180717-9-6.


Cite as: http://hdl.handle.net/21.11116/0000-0008-ADF2-4
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 Andr\'e-Oort conjecture.