Even Galois representations and the Fontaine-Mazur conjecture

• 成果类型: Article
• 署名作者: Calegari, Frank
• 署名单位: Northwestern University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0297-0
• 发表日期: 2011
• 页码: 1-16
• 关键词: l-adic lifts; automorphy

摘要

We prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of Gal((Q) over bar /Q) with distinct Hodge-Tate weights. This is in accordance with the Fontaine-Mazur conjecture. If K/Q is an imaginary quadratic field, we also prove ( again, under certain hypotheses) that Gal((Q) over bar /K) does not admit irreducible two-dimensional ordinary Galois representations of non-parallel weight.