Motives with exceptional Galois groups and the inverse Galois problem

Zhiwei Yun

Motives with exceptional Galois groups and the inverse Galois problem

Number Theory 2011-12-13 v1 Algebraic Geometry

Authors: Zhiwei Yun

Abstract

We construct motivic $\ell$ -adic representations of $\GQ$ into exceptional groups of type $E_7,E_8$ and $G_2$ whose image is Zariski dense. This answers a question of Serre. The construction is uniform for these groups and uses the Langlands correspondence for function fields. As an application, we solve new cases of the inverse Galois problem: the finite simple groups $E_{8}(\FF_{\ell})$ are Galois groups over $\QQ$ for large enough primes $\ell$ .

Keywords

motivic representations exceptional Galois groups inverse Galois problem Langlands correspondence Zariski dense finite simple groups ℓ-adic representations

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@article{arxiv.1112.2434,
  title  = {Motives with exceptional Galois groups and the inverse Galois problem},
  author = {Zhiwei Yun},
  journal= {arXiv preprint arXiv:1112.2434},
  year   = {2011}
}

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40 pages

Motives with exceptional Galois groups and the inverse Galois problem

Abstract

Keywords

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