Base change for Hilbert eigenvarieties of unitary groups

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.