Représentations localement analytiques de GL 3 ( p )
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 44 (2011) no. 1, pp. 43-145.

Nous construisons un complexe de représentations localement analytiques de GL 3 ( p ), associé à certaines représentations semi-stables de dimension 3 du groupe de Galois absolu de p . Nous montrons ensuite que l’on peut retrouver le (ϕ,N)-module filtré de la représentation galoisienne en considérant les morphismes, dans la catégorie dérivée des D( GL 3 ( p ))-modules, de ce complexe dans le complexe de de Rham de l’espace de Drinfel’d de dimension 2. La preuve requiert le calcul de certains espaces de cohomologie localement analytiques de sous-groupes unipotents à coefficients dans des séries principales localement analytiques.

We construct a complex of locally analytic representations of GL 3 ( p ), which is associated to some semi-stable 3-dimensional representations of the absolute Galois group of p . Then we show that we can retrieve the (ϕ,N)-filtered module of the Galois representation in the space of morphisms, in the derived category of D( GL 3 ( p ))-modules, of this complex in the de Rham-complex of the 2-dimensional Drinfel’d’s space. For the proof, we compute some spaces of locally analytic cohomology of unipotent subgroups with coefficients in some locally analytic principal series.

DOI : 10.24033/asens.2140
Classification : 11F70, 11S20, 11S37, 11S80, 14G22, 22E50
Mot clés : correspondance de Langlands $p$-adique, espaces de Drinfel’d, représentations localement analytiques $p$-adiques
Keywords: $p$-adic Langlands correspondence, Drinfel’d’s spaces, $p$-adic locally analytic representations
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     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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Schraen, Benjamin. Représentations localement analytiques de $\mathrm {GL}_3(\mathbb {Q}_{p})$. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 44 (2011) no. 1, pp. 43-145. doi : 10.24033/asens.2140. http://archive.numdam.org/articles/10.24033/asens.2140/

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