On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms

Abstract

We prove Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and refinement of the results of Grobner and Lin to cohomological irreducible essentially conjugate self-dual cuspidal automorphic representations of ${\rm GL}_2$ and ${\rm GL}_3$ over CM-fields.Comment: arXiv admin note: text overlap with arXiv:2012.0062