Langlands base change for $\mathrm{GL}(2)$


Let $F$ be a totally real Galois number field. We prove the existence of base change relative to the extension $F/\mathbb{Q}$ for every holomorphic newform of weight at least $2$ and odd level, under simple local assumptions on the field $F$.


Luis Dieulefait

Departament d'Àlgebra i Geometria, Universitat de Barcelona
Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain