1. CJM 2012 (vol 65 pp. 403)
|On the Dihedral Main Conjectures of Iwasawa Theory for Hilbert Modular Eigenforms|
We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel weight two over totally real fields, generalizing works of Bertolini-Darmon, Longo, Nekovar, Pollack-Weston and others. The construction has direct applications to Iwasawa main conjectures. For instance, it implies in many cases one divisibility of the associated dihedral or anticyclotomic main conjecture, at the same time reducing the other divisibility to a certain nonvanishing criterion for the associated $p$-adic $L$-functions. It also has applications to cyclotomic main conjectures for Hilbert modular forms over CM fields via the technique of Skinner and Urban.
Keywords:Iwasawa theory, Hilbert modular forms, abelian varieties
Categories:11G10, 11G18, 11G40
2. CJM 2011 (vol 64 pp. 588)
|Level Raising and Anticyclotomic Selmer Groups for Hilbert Modular Forms of Weight Two|
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
Categories:11G40, 11F41, 11G18