Intersection of class fields

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Intersection of class fields. / Kühne, Lars.

In: Acta Arithmetica, Vol. 198, No. 2, 2021, p. 109-127.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kühne, L 2021, 'Intersection of class fields', Acta Arithmetica, vol. 198, no. 2, pp. 109-127. https://doi.org/10.4064/aa180717-9-6

APA

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

Vancouver

Kühne L. Intersection of class fields. Acta Arithmetica. 2021;198(2):109-127. https://doi.org/10.4064/aa180717-9-6

Author

Kühne, Lars. / Intersection of class fields. In: Acta Arithmetica. 2021 ; Vol. 198, No. 2. pp. 109-127.

Bibtex

@article{3ad4da45f1de4f9c853a649d4b84394c,
title = "Intersection of class fields",
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.",
author = "Lars K{\"u}hne",
year = "2021",
doi = "10.4064/aa180717-9-6",
language = "English",
volume = "198",
pages = "109--127",
journal = "Acta Arithmetica",
issn = "0065-1036",
publisher = "Polska Akademia Nauk Instytut Matematyczny",
number = "2",

}

RIS

TY - JOUR

T1 - Intersection of class fields

AU - Kühne, Lars

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

U2 - 10.4064/aa180717-9-6

DO - 10.4064/aa180717-9-6

M3 - Journal article

VL - 198

SP - 109

EP - 127

JO - Acta Arithmetica

JF - Acta Arithmetica

SN - 0065-1036

IS - 2

ER -

ID: 305404368