On a theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over genus fields of real quadratic fields

Mok, Chung

doi:10.1090/tran/8254

On a theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over genus fields of real quadratic fields

Author: Chung Pang Mok
Journal: Trans. Amer. Math. Soc. 374 (2021), 1391-1419
MSC (2020): Primary 11G05, 11G40
DOI: https://doi.org/10.1090/tran/8254
Published electronically: November 25, 2020
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Abstract: In this paper, we remove certain hypotheses in the theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over narrow genus class fields of real quadratic fields. Along the way, we establish that certain normalized special values of -functions are squares of rational numbers, a result that is of independent interest, and can be regarded as instances of the rank zero case of the Birch and Swinnerton-Dyer conjecture modulo squares.

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