Rendiconti del Seminario Matematico della Università di Padova


Full-Text PDF (240 KB) | Metadata | Table of Contents | RSMUP summary
Volume 137, 2017, pp. 135–153
DOI: 10.4171/RSMUP/137-7

Strong local-global compatibility in the $p$-adic Langlands program for $U(2)$

Przemyslaw Chojecki[1] and Claus Sorensen[2]

(1) Oxford University, UK
(2) University of California, San Diego, USA

For certain mod $p$ Galois representations $\bar{\rho}$, arising from modular forms on definite unitary groups in two variables, we express the $\bar{\rho}$-part of completed cohomology $\widehat{H}_{\bar{\rho}}^0$ (away from $\Sigma=\Sigma_p\cup \Sigma_0$) as a tensor product $\Pi_p\otimes \Pi_{\Sigma_0}$. Here $\Pi_p$ is attached to the universal deformation $\rho^{univ}$ via the $p$-adic local Langlands correspondence for GL$_2(\mathbb Q_p)$, and $\Pi_{\Sigma_0}$ is given by the local Langlands correspondence in families, of Emerton and Helm.

Keywords: Galois representations, automorphic forms, $p$-adic Langlands program

Chojecki Przemyslaw, Sorensen Claus: Strong local-global compatibility in the $p$-adic Langlands program for $U(2)$. Rend. Sem. Mat. Univ. Padova 137 (2017), 135-153. doi: 10.4171/RSMUP/137-7