Base change for Hilbert eigenvarieties of unitary groups

The construction of eigenvarieties due to Chenevier is extended to the Hilbert case, that is, to unitary groups over a totally real field F that are anisotropic at each archimedean place. This permits us to ask about the relationship of the eigenvarieties that we construct for two totally real fields, one being a cyclic extension of the other. Bibliography: 23 titles.