Ordinarity of Local Galois Representation Arising from Dwork Motives

2021/02/27 by Lie Qian, Qian, Lie
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2103.00106

Abstract

In this paper, we prove that for suitably chosen Dwork motives, the local Galois representation arising from middle cohomology of fibers over a point with p-adic valuation <0 on the base is regular and ordinary. The result will be crucial in the forthcoming work Potential Automorphy for GL_n. The proof consists of the construction of a semistable blowup and a use of Hyodo-Kato's log crystalline cohomology theory.

Related

• Dwork Motives, Monodromy and Potential Automorphy
• Potential Automorphy for GL_n
• The residual monodromy for the Dwork family in even characteristic and its applications to Galois representations
• Potential automorphy for certain Galois representations to GL₂n
• Local Shtukas, Hodge-Pink Structures and Galois Representations