The residual monodromy for the Dwork family in even characteristic and its applications to Galois representations

2025/06/30 by Yamauchi, Takuya
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2506.23938

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the residual monodromy representations associated to the Dwork family in characteristic two. Various applications involving 2-adic and mod 2 Galois representations are discussed. Combining the author's previous work with Tsuzuki and recent results of Boxer, Calegari, Gee, and Pilloni, we also prove the automorphy of certain rank 4 symplectic motives over a totally real field, arising from the Dwork quintic family, under suitable conditions.

Citations

• Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
• Automorphy lifting with adequate image
• Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials
• Reductions of some two-dimensional crystalline representations via Kisin\n modules
• Potential automorphy over CM fields
• Abelian Surfaces over totally real fields are Potentially Modular
• Variations on a theorem of Tate
• A Note on Potential Diagonalizability of Crystalline Representations
• On the automorphy of l-adic Galois representations with small residual\n image
• Irreducibility of automorphic Galois representations of GL(n), n at most\n 5
• Potential automorphy and change of weight
• The Sato-Tate conjecture for Hilbert modular forms
• On the Zeta Function of a Family of Quintics
• Meromorphic continuation for the zeta function of a Dwork hypersurface
• Compatibility of local and global Langlands correspondences
• Construction of some families of 2-dimensional crystalline representations
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Abelian varieties over Q and modular forms

Related

• Dwork Motives, Monodromy and Potential Automorphy
• Ordinarity of Local Galois Representation Arising from Dwork Motives
• Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials
• Mod pq Galois representations and Serre's conjecture
• Automorphy of some residually S₅ Galois representations