GL₂(ℚ_p)-ordinary families and automorphy lifting

2019/07/17 by Yiwen Ding, Ding, Yiwen
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1907.07372

openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove automorphy lifting results for certain essentially conjugate self-dual p-adic Galois representations ρ over CM imaginary fields F, which satisfy in particular that p splits in F, and that the restriction of ρ on any decomposition group above p is reducible with all the Jordan-Hölder factors of dimension at most 2. We also show some results on Breuil's locally analytic socle conjecture in certain non-trianguline case. The main results are obtained by establishing an R=\mathbbT-type result over the GL₂(ℚ_p)-ordinary families considered by Breuil-Ding.

Citations

• On the automorphy of l-adic Galois representations with small residual image

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