222 research outputs found

    Motives with exceptional Galois groups and the inverse Galois problem

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    We construct motivic β„“\ell-adic representations of \GQ into exceptional groups of type E7,E8E_7,E_8 and G2G_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 β„“\ell.Comment: 40 page

    The fundamental lemma of Jacquet-Rallis in positive characteristics

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    We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is greater than the rank of the relevant groups.Comment: 40 pages; Both the group Version and the Lie algebra version are prove
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