On non-admissible irreducible modulo $p$ representations of ${\mathrm{GL}}_2\left({\mathbb{Q}}_{p^2}\right)$

Ghate, Eknath; Sheth, Mihir

Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 627-632.

Nous utilisons un diagramme de Diamond attaché à une représentation galoisienne mod $p$ semi-simple réductible de dimension 2 de $\mathrm{Gal}(\overline{{\mathbb{Q}}_p}/{\mathbb{Q}}_{p^2})$ pour construire une représentation mod $p$ non-admissible irréductible lisse de ${\mathrm{GL}}_2\left({\mathbb{Q}}_{p^2}\right)$ en suivant l’approche de Daniel Le.

We use a Diamond diagram attached to a 2-dimensional reducible split mod $p$ Galois representation of $\mathrm{Gal}(\overline{{\mathbb{Q}}_p}/{\mathbb{Q}}_{p^2})$ to construct a non-admissible smooth irreducible mod $p$ representation of ${\mathrm{GL}}_2\left({\mathbb{Q}}_{p^2}\right)$ following the approach of Daniel Le.

Classification : 22E50, 11S37

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