Modularity Proof Without Ihara's Lemma

Generalizing modularity lifting theorems for higher-dimensional Galois representations

Abstract

The title is "Proving modularity without Ihara's lemma",which is the subject of the preprint. "A family of Calabi-Yau varieties and the Sato-Tate conjecture". The aim ofresearch paper is to generalize the modularity lifting theorems of higherdimensional Galois representations.