In this article we refine the method of Bertolini and Darmon and prove several finiteness results for anticyclotomic Selmer groups of Hilbert modular forms of parallel weight two.

Keywords:

Hilbert modular forms, Selmer groups, Shimura curves Hilbert modular forms, Selmer groups, Shimura curves

MSC Classifications:

11G40, 11F41, 11G18 show english descriptions $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
Automorphic forms on ${\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Arithmetic aspects of modular and Shimura varieties [See also 14G35] 11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
11F41 - Automorphic forms on ${\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
11G18 - Arithmetic aspects of modular and Shimura varieties [See also 14G35]

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