Motives with exceptional Galois groups and the inverse Galois problem

By Zhiwei Yun. 2011

60 citations recorded by the source corpus.

We construct motivic ℓ-adic representations of $\textup {Gal}(\overline {\mathbb{Q}}/\mathbb{Q})$ into exceptional groups of type E7,E8 and G2 whose image is Zariski dense. This answers a question of Serre. The construction is uniform for these groups and is inspired by the Langlands correspondence for function fields. As an application, we solve new cases of the inverse Galois problem: the finite simple groups $E_{8}(\mathbb{F}_{\ell})$ are Galois groups over $\mathbb{Q}$ for large enough primes ℓ.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a879481a89c7a1300932adff84f643c89e87c944

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In Geometry and Topology

1. Tasho Kaletha
2. Jessica Fintzen
3. Mark Reeder
4. J. Yu

In Mathematical Physics

1. Tasho Kaletha
2. Jessica Fintzen
3. Mark Reeder
4. J. Yu

Citations in the corpus

• Epipelagic $$L$$L-packets and rectifying characters (2012, methodology): “In subsequent work, Yun [57] uses epipelagic representations of depth 1/2 to construct in motivic Galois groups of exceptional type, and obtain results towards the inverseGalois problem.”