Heisenberg varieties and the existence of de Rham lifts

Abstract

We establish the existence of de Rham lifts of Langlands parameters (or Galois representations) for unitary, orthogonal and symplectic (similitude) groups of arbitrary rank. Our results are unconditional except for the assumption $p>2$.

Compared to v1, we expanded the scope to all classical groups instead of just unitary groups and the last section was isolated into arXiv:2508.19722