Bibliographic Details
| Title: |
Modular supercuspidal lifts of weight 2. |
| Authors: |
Blanco-Chacón, Iván1 (AUTHOR) ivan.blancoc@uah.es, Dieulefait, Luis2 (AUTHOR) ldieulefait@ub.edu |
| Source: |
Journal of Number Theory. Aug2026, Vol. 285, p54-73. 20p. |
| Subjects: |
Modular forms, Number theory, Representation theory |
| Abstract: |
Let F / Q be a totally real number field and N an ideal of its ring of integers of norm N. Let p > max { k + 1 , 6 } be a prime totally split in F such that p ∤ N. For every even k ≥ 2 , define the [ F : Q ] -dimensional parallel weight k = (k ,... , k). Let f ∈ S k (Γ 0 (N)) be any non CM Hilbert cuspidal Hecke eigenform. Assume that the residual representation ρ ‾ f , P has large image for some prime P over p in the field of definition of f. Under these conditions, we prove that there exists a lift of ρ ‾ f , P associated to a Hilbert modular cuspform g ∈ S 2 (N p 2 , ϵ) which is supercuspidal at each prime of F over p. We also give a proof of the corresponding statement for classical Hecke cuspforms. Such statement was already proved by Khare [23] with classical techniques. Finally, using our main result we give a corrigenda for [12] , correctly inserting the micro good dihedral prime in the level. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
