Motives with exceptional Galois groups and the inverse Galois problem

• 成果类型: Article
• 署名作者: Yun, Zhiwei
• 署名单位: Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0469-9
• 发表日期: 2014
• 页码: 267-337
• 关键词: 6 operations; sheaves; REPRESENTATIONS; cells

摘要

We construct motivic a-adic representations of 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 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 are Galois groups over for large enough primes a.