Motives with exceptional Galois groups and the inverse Galois problem

2011/12/12 by Zhiwei Yun, Yun, Zhiwei · 1 citation
Mathematics · #11F80 #14D24 #20G41 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1112.2434

openalex publication_date 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct motivic ℓ-adic representations of \GQ 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 uses the Langlands correspondence for function fields. As an application, we solve new cases of the inverse Galois problem: the finite simple groups E₈(\FF_ℓ) are Galois groups over \QQ for large enough primes ℓ.

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