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

Eknath Ghate; Mihir Sheth

doi:10.5802/crmath.85

Théorie des nombres et théorie des groupes réductifs

On non-admissible irreducible modulo

p

representations of

{GL}_{2} (ℚ_{p^{2}})

[Sur les représentations irréductibles non-admissibles modulo

p

de

{GL}_{2} (ℚ_{p^{2}})

]

Eknath Ghate ¹ ; Mihir Sheth ¹

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400005, India

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

Abstract (VO)
Résumé

We use a Diamond diagram attached to a 2-dimensional reducible split mod $p$ Galois representation of $Gal (\bar{ℚ_{p}} / ℚ_{p^{2}})$ to construct a non-admissible smooth irreducible mod $p$ representation of ${GL}_{2} (ℚ_{p^{2}})$ following the approach of Daniel Le.

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

Reçu le : 2020-03-12
Accepté le : 2020-06-09
Publié le : 2020-09-14

DOI : 10.5802/crmath.85

Classification : 22E50, 11S37

Affiliations des auteurs :

Eknath Ghate ¹ ; Mihir Sheth ¹

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400005, India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Eknath Ghate and Mihir Sheth},
     title = {On non-admissible irreducible modulo $p$ representations of $\protect \mathrm{GL}_{2}(\protect \mathbb{Q}_{p^{2}})$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {627--632},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {5},
     year = {2020},
     doi = {10.5802/crmath.85},
     language = {en},
}

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Eknath Ghate; Mihir Sheth. On non-admissible irreducible modulo $p$ representations of $\protect \mathrm{GL}_{2}(\protect \mathbb{Q}_{p^{2}})$. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 627-632. doi : 10.5802/crmath.85. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.85/

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