In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galois group to a subgroup.
Base change lifting was introduced by Hiroshi Saito (1975, 1975b, 1979) for Hilbert modular forms of cyclic totally real fields of prime degree, by comparing the trace of twisted Hecke operators on Hilbert modular forms with the trace of Hecke operators on ordinary modular forms.
Shintani (1979) gave a representation theoretic interpretation of Saito's results and used this to generalize them.
Langlands (1980) extended the base change lifting to more general automorphic forms and showed how to use the base change lifting for GL2 to prove the Artin conjecture for tetrahedral and some octahedral 2-dimensional representations of the Galois group.
If E/F is a finite cyclic Galois extension of global fields, then the base change lifting of Arthur & Clozel (1989) gives a map from automorphic forms for GLn(F) to automorphic forms for GLn(E) = ResE/FGLn(F).