## The unitary principal series of $$\text{GL}_2 (\mathbb Q_p)$$. (La série principale unitaire de $$\text{GL}_2 (\mathbb Q_p)$$.)(French. English summary)Zbl 1242.11095

Berger, Laurent (ed.) et al., Représentations $$p$$-adiques de groupes $$p$$-adiques II: Représentations de $$\text{GL}_2 (\mathbb Q_p)$$ et $$(\varphi, \gamma)$$-modules. Paris: Société Mathématique de France (ISBN 978-2-85629-281-5/pbk). Astérisque 330, 213-262 (2010).
This paper is devoted to the $$p$$-adic local Langlands correspondence for the unitary principal series of $$\text{GL}_2 (\mathbb Q_p)$$. The author uses Fontaine’s theory of $$(\varphi,\Gamma)$$-modules to establish, in the semistable and non geometric cases, a direct link between the (dual of) representation of $$\text{GL}_2 (\mathbb Q_p)$$ and the $$(\varphi,\Gamma)$$-module attached to the representation of $$\text{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)$$.
For the entire collection see [Zbl 1192.11001].

### MSC:

 11S37 Langlands-Weil conjectures, nonabelian class field theory

### Keywords:

local Langlands correspondence
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