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- W2978352051 abstract "Let $X$ be a smooth, projective, geometrically connected curve over a finite field $mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $mathbb{F}_q$. Its dual group $widehat{G}$ is a split reductive group over $mathbb{Z}$. Conjecturally, any $l$-adic $widehat{G}$-local system on $X$ (equivalently, any conjugacy class of continuous homomorphisms $pi_1(X) to widehat{G}(overline{mathbb{Q}}_l)$) should be associated with an everywhere unramified automorphic representation of the group $G$. We show that for any homomorphism $pi_1(X) to widehat{G}(overline{mathbb{Q}}_l)$ of Zariski dense image, there exists a finite Galois cover $Y to X$ over which the associated local system becomes automorphic." @default.
- W2978352051 created "2019-10-10" @default.
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- W2978352051 date "2019-01-01" @default.
- W2978352051 modified "2023-10-13" @default.
- W2978352051 title "$hat{G}$-local systems on smooth projective curves are potentially automorphic" @default.
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- W2978352051 doi "https://doi.org/10.4310/acta.2019.v223.n1.a1" @default.
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