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

Abstract

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 $F$.

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      ARXIV= {math.NT/0406576},
     }

Authors

Luis Dieulefait

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