Potential Automorphy for GL_n

2021/04/20 by Lie Qian, Qian, Lie
Arts and Humanities · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.09761

openalex publication_date 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove potential automorphy results for a single Galois representation G_F → GL_n(ℚ_l) where F is a CM number field. The strategy is to use the p,q switch trick and modify the Dwork motives employed in \citeHSBT to break self-duality of the motives, but not the Hodge-Tate weights. Another key result to prove is the ordinarity of certain p-adic representations, which follows from log geometry techniques. One input is the automorphy lifting theorem in \citetap.

Related

• Potential automorphy over CM fields
• Potential automorphy for certain Galois representations to GL₂n
• Potential automorphy of certain non self-dual 3-dimensional Galois representations
• Potential automorphy and change of weight
• Potential automorphy of GSpin_2n+1-valued Galois representations