Level lowering for GU(1,2)

2022/11/12 by Hao Fu, Fu, Hao
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2211.06673

openalex publication_date 2022/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mazur's principle gives a criterion under which an irreducible mod ℓ Galois representation arising from a modular form of level Np (with p prime to N) can also arise from a modular form of level N. We prove an analogous result showing that a mod ℓ Galois representation arising from a stable cuspidal automorphic representation of the unitary similitude group G=GU(1,2) which is Steinberg at an inert prime p can also arise from an automorphic representation of G that is unramified at p.

Related

• Mazur's principle for U(2,1) Shimura varieties
• A level raising result for modular Galois representations modulo prime powers
• Level lowering: a Mazur principle in higher dimension
• Non-optimal levels of a reducible mod l modular representation
• Congruences between modular forms and lowering the level mod lⁿ