On \(l\)-adic representations attached to Hilbert and Picard modular surfaces
type: Item
instance of: scholarly article
title: On \(l\)-adic representations attached to Hilbert and Picard modular surfaces
zbMATH Open document ID: 1229.11085
author: Cristian Virdol
published in: Journal of Number Theory
publication date: 2010-05-17T00:00:00Z
review text: Let \(L\) be a real quadratic number field and \(\pi\) a cohomological cuspidal automorphic representation of \(\mathrm{Res}_{L|\mathbb{Q}}\text{GL}(2)\) of weight 2. And let \(F\) be a totally real number field, \(E\) an imaginary quadratic extension of \(F\), and \(\Pi_f\) the finite component of a cohomological discrete series automorphic representation of \(\text{GU}(3)\) defined relative to \(E\mid F\). Under the assumption that \(F\) does not contain \(L\), the author computes the \(\ell\)-adic Lie algebra of the image of \(\Gamma_E=\mathrm{Gal}(\bar{\mathbb{Q}}| E)\) under the product \(\rho(\pi)|_{\Gamma_E}\times\phi(\Pi_f)\) of \(\ell\)-adic Galois representations associated with \(\pi\) and \(\Pi_f\) respectively. The author's approach is analogous to that of \textit{K. Ribet} [Math. Ann. 253, 43--62 (1980; Zbl 0421.14008)] for weight 2 eigenforms of \(\text{SL}(2)\).
reviewed by: Gerald Gotsbacher
Mathematics Subject Classification ID: 11F80
Mathematics Subject Classification ID: 11F41
Mathematics Subject Classification ID: 11G18
zbMATH DE Number: 5708638
zbMATH Keywords: \(\ell\)-adic representation
zbMATH Keywords: \(\ell\)-adic Lie algebra
zbMATH Keywords: Hilbert modular surface
zbMATH Keywords: Picard modular surface
MaRDI profile type: Publication
full work available at URL: j.jnt.2009.10.006
OpenAlex ID: W2005453557
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DOI: 10.1016/J.JNT.2009.10.006
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description: scientific article; zbMATH DE number 5708638