Moduli stacks of Galois representations and the p -adic local Langlands correspondence for

Journal article

We give a categorical formulation of the p-adic local Langlands correspondence for as an embedding of the derived category of locally admissible representations into the category of Ind-coherent sheaves on the moduli stack of two-dimensional representations of . The Montréal functor appears as the‘Whittaker coefficient’ for the universal Galois representation, in the sense of the geometric Langlands program. Moreover, we relate our version of the p-adic local Langlands correspondence for to the cohomology of modular curves through a local–global compatibility formula.

Authors: Johansson, C; Newton, J; Wang-Erickson, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Compositio Mathematica
• Volume: 162
• Issue: 2
• Pages: 368-450
• Publication date: 2026-06-17
• Acceptance date: 2025-09-24
• DOI: 10.1017/s0010437x2610298x
• EISSN: 1570-5846
• ISSN: 0010437X, 0010-437X
• Language: English
• Keywords: 11F80; p-adic local Langlands correspondence; geometrization of the Langlands correspondence; 11F85; 11S37; 22E50; Galois representations; moduli stacks