1. CJM 2014 (vol 67 pp. 315)
|Unitary Eigenvarieties at Isobaric Points|
In this article we study the geometry of the eigenvarieties of unitary groups at points corresponding to tempered non-stable representations with an anti-ordinary (a.k.a evil) refinement. We prove that, except in the case the Galois representation attached to the automorphic form is a sum of characters, the eigenvariety is non-smooth at such a point, and that (under some additional hypotheses) its tangent space is big enough to account for all the relevant Selmer group. We also study the local reducibility locus at those points, proving that in general, in contrast with the case of the eigencurve, it is a proper subscheme of the fiber of the eigenvariety over the weight space.
Keywords:eigenvarieties, Galois representations, Selmer groups
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