Potential automorphy for G Ln
成果类型：
Article
署名作者：
Qian, Lie
署名单位：
Stanford University
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-022-01161-6
发表日期：
2023
页码：
1239-1275
关键词：
摘要：
We prove potential automorphy results for a single Galois representation G(F) -> GL(n)((Q) over bar (l)) where F is a CM number field. The strategy is to use the p, q switch trick to go between the p-adic and q-adic realisation of a certain variant of the Dwork motive. We choose this variant to break self-duality shape of the motives, but not the Hodge-Tate weights. Another key result to prove is that certain p-adic representations we choose that come from the Dwork motives is ordinarily automorphic. One input is the automorphy lifting theorem in Allen et al.: (Potential automorphy over CM fields, Cornell University, New York 2018).
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