Canadian Mathematical Society
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Unitary Eigenvarieties at Isobaric Points

 Printed: Apr 2015
  • Joël Bellaïche,
    Department of Mathematics, Brandeis University, 415 South Street, Waltham, MA 02454-9110, U.S.A
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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 eigenvarieties, Galois representations, Selmer groups

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