Heisenberg varieties and the existence of de Rham lifts

TL;DR

This paper proves the existence of de Rham lifts for Galois representations associated with various classical groups, advancing understanding in number theory and the Langlands program.

Contribution

It establishes unconditional existence results for de Rham lifts of Langlands parameters for classical groups, assuming only that p>2.

Findings

De Rham lifts exist for Galois representations of unitary, orthogonal, and symplectic groups.

Results are unconditional except for the prime p>2.

Advances the understanding of Galois representations in the Langlands correspondence.

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 $p>2$.