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

  • Przemyslaw Chojecki

    Oxford University, UK
  • Claus Sorensen

    University of California, San Diego, USA

Abstract

For certain mod pp Galois representations ρˉ\bar{\rho}, arising from modular forms on definite unitary groups in two variables, we express the ρˉ\bar{\rho}-part of completed cohomology H^ρˉ0\widehat{H}_{\bar{\rho}}^0 (away from Σ=ΣpΣ0\Sigma=\Sigma_p\cup \Sigma_0) as a tensor product ΠpΠΣ0\Pi_p\otimes \Pi_{\Sigma_0}. Here Πp\Pi_p is attached to the universal deformation ρuniv\rho^{univ} via the pp-adic local Langlands correspondence for GL2(Qp)_2(\mathbb Q_p), and ΠΣ0\Pi_{\Sigma_0} is given by the local Langlands correspondence in families, of Emerton and Helm.

Cite this article

Przemyslaw Chojecki, Claus Sorensen, Strong local-global compatibility in the pp-adic Langlands program for U(2)U(2). Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 135–153

DOI 10.4171/RSMUP/137-7