An approach to nonsolvable base change and descent

Abstract

We present a collection of conjectural trace identities and explain why they are equivalent to base change and descent of automorphic representations of ${\mathrm{GL}}_n({\mathbb{A}}_F)$ along nonsolvable extensions (under some simplifying hypotheses). The case $n=2$ is treated in more detail and applications towards the Artin conjecture for icosahedral Galois representations are given.

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