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
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Trans. Amer. Math. Soc. 374 (2021), 1391-1419 Request permission

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 $L$-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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