Unitary Eigenvarieties at Isobaric Points

Bellaïche, Joël

Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 315-329

Résumé

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 where 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.

Détail

DOI : 10.4153/CJM-2014-020-9

Mots-clés : 11S25, Eigenvarieties, Galois representations, Selmer groups

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