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

Abstract

We prove an automorphic analogue of 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 ${\mathrm{GL}}_2$ and ${\mathrm{GL}}_3$ over CM-fields.

arXiv commentto be published in Advances in Mathematics. arXiv admin note: text overlap with arXiv:2012.00625

References in corpus (4)

• Cohomologically induced distinguished representations and cohomological test vectors
• Whittaker rational structures and special values of the Asai $L$-function
• Coherent cohomology of Shimura varieties and automorphic forms
• Algebraicity of the near central non-critical value of symmetric fourth $L$-functions for Hilbert modular forms