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# Level Raising and Anticyclotomic Selmer Groups for Hilbert Modular Forms of Weight Two

Published:2011-11-15
Printed: Jun 2012
• Jan Nekovář,
Université Pierre et Marie Curie (Paris 6), Institut de Mathématiques de Jussieu, Paris, FRANCE
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## Abstract

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
 MSC Classifications: 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]