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

TL;DR

This paper investigates the residual monodromy representations of the Dwork family in characteristic two and applies these findings to establish automorphy results for certain Galois representations and motives.

Contribution

It introduces new results on residual monodromy in characteristic two and proves automorphy of specific rank 4 symplectic motives related to the Dwork family.

Findings

Residual monodromy representations in characteristic two are characterized.

Automorphy of certain rank 4 symplectic motives is established.

Connections between monodromy, Galois representations, and automorphy are demonstrated.

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.