Geodesic
Base change for Hilbert eigenvarieties of unitary groups
Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 10, Tome 377 (2010), pp. 148-198

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The construction of eigenvarieties by Chenevier is extended to the Hilbert case, that is to unitary groups over a totally real field $F$ which are anisotropic at each archimedean place. This permits us to ask about the relationship of the eigenvarieties which we construct for two totally real fields, one being a cyclic extension of the other. Bibl. 23 titles. 
@article{ZNSL_2010_377_a14,
     author = {Yu. Z. Flicker},
     title = {Base change for {Hilbert} eigenvarieties of unitary groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {148--198},
     publisher = {mathdoc},
     volume = {377},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_377_a14/}
}
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Yu. Z. Flicker. Base change for Hilbert eigenvarieties of unitary groups. Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 10, Tome 377 (2010), pp. 148-198. http://geodesic.mathdoc.fr/item/ZNSL_2010_377_a14/