Non-abelian base change for symmetric power liftings of holomorphic modular forms

2023/12/04 by Laurent Clozel, Clozel, Laurent, James Newton +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.01774

openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a non-CM Hecke eigenform of weight k ≥ 2. We give a new proof of some cases of Langlands functoriality for the automorphic representation π associated to f. More precisely, we prove the existence of the base change lifting, with respect to any totally real extension F / ℚ, of any symmetric power lifting of π.

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