- journal article metadata
European Mathematical Society Publishing House
2017-05-15 23:45:01
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
137
2017
0
Strong local-global compatibility in the $p$-adic Langlands program for $U(2)$
Przemyslaw
Chojecki
Oxford University, OXFORD, UNITED KINGDOM
Claus
Sorensen
University of California, San Diego (UCSD), LA JOLLA, UNITED STATES
Galois representations, automorphic forms, $p$-adic Langlands program
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.
Number theory
135
153
10.4171/RSMUP/137-7
http://www.ems-ph.org/doi/10.4171/RSMUP/137-7