A p$p$‐adic approach to the existence of level‐raising congruences

Abstract

AbstractWe construct level‐raising congruences between ‐ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer . In a future work with James Newton, we will use these results to establish the existence of the symmetric power lift for all .