We construct nonsmooth points on unitary eigenvarieties. More precisely, we construct points so that the local ring of the irreducible components of the eigenvariety through this point is nonsmooth and not even a unique factorization domain (UFD). We use those points to construct geometrically several independent extensions in the relevant Selmer group
Duke Math. J.
145(1):
71-90
(1 October 2008).
DOI: 10.1215/00127094-2008-047
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