Geodesic
Unitary Eigenvarieties at Isobaric Points
Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 315-329

Voir la notice de l'article provenant de la source Cambridge

DOI

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.
DOI : 10.4153/CJM-2014-020-9
Mots-clés : 11S25, Eigenvarieties, Galois representations, Selmer groups 
Bellaïche, Joël. Unitary Eigenvarieties at Isobaric Points. Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 315-329. doi: 10.4153/CJM-2014-020-9
@article{10_4153_CJM_2014_020_9,
     author = {Bella{\"\i}che, Jo\"el},
     title = {Unitary {Eigenvarieties} at {Isobaric} {Points}},
     journal = {Canadian journal of mathematics},
     pages = {315--329},
     year = {2015},
     volume = {67},
     number = {2},
     doi = {10.4153/CJM-2014-020-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-020-9/}
}
TY  - JOUR
AU  - Bellaïche, Joël
TI  - Unitary Eigenvarieties at Isobaric Points
JO  - Canadian journal of mathematics
PY  - 2015
SP  - 315
EP  - 329
VL  - 67
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-020-9/
DO  - 10.4153/CJM-2014-020-9
ID  - 10_4153_CJM_2014_020_9
ER  - 
%0 Journal Article
%A Bellaïche, Joël
%T Unitary Eigenvarieties at Isobaric Points
%J Canadian journal of mathematics
%D 2015
%P 315-329
%V 67
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-020-9/
%R 10.4153/CJM-2014-020-9
%F 10_4153_CJM_2014_020_9

Cité par Sources :