2023/10/17 by Iván Blanco-Chacón, Blanco-Chacón, Iván, Luís Dieulefait +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2310.11522
openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F/ℚ be any totally real number field and \frakN an ideal of its ring of integers of norm N and define, for every even n, the [F:ℚ]-dimensional multiweight n=(n,...,n). We prove that for a non CM Hilbert cuspidal Hecke eigenform for F, say f∈ Sk(Γ0(\frakN)) with k>2 even, and a prime p>max\k+1,6\ totally split in F such that p\nmid N and such that the residual mod p representation ρf satisfies that SL2(\mathbbFp)⊆ Im(ρf), there exists a lift ρg associated to a Hilbert modular cuspform for F, say g∈ S2(\frakNp2,ε) for some Nebentypus character ε which is supercuspidal at each prime of F over p. We also observe that our techniques provide an alternative proof to the corresponding statement for classical Hecke cuspforms already proved by Khare \citekhare with classical techniques. Finally, we take the opportunity to include a corrigenda for \citedieulefait which follows from our main result, which provides a congruence that puts the micro good dihedral prime in the level.