Title: 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.