Weight reduction for cohomological mod p modular forms over imaginary quadratic fields

2011/08/23 by Adam Mohamed, Mohamed, Adam
Mathematics · #11-XX #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.NT #msc:11-XX

paper · pdf · doi:10.48550/arxiv.1108.4619

30 pages

arxiv created 2011/08/23 · openalex publication_date 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let F be an imaginary quadratic field and O its ring of integers. Let \mathfrakn ⊂ O be a non-zero ideal and let p> 5 be a rational inert prime in F and coprime with \mathfrakn. Let V be an irreducible finite dimensional representation of \mathbbF_p[\rm GL₂(\mathbbF_p²)]. We establish that a system of Hecke eigenvalues appearing in the cohomology with coefficients in V already lives in the cohomology with coefficients in \mathbbF_p⊗ det^e for some e ≥ 0; except possibly in some few cases.

Citations

• Hasse invariant and group cohomology

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