We use a Diamond diagram attached to a 2-dimensional reducible split mod Galois representation of to construct a non-admissible smooth irreducible mod representation of following the approach of Daniel Le.
Nous utilisons un diagramme de Diamond attaché à une représentation galoisienne mod semi-simple réductible de dimension 2 de pour construire une représentation mod non-admissible irréductible lisse de en suivant l’approche de Daniel Le.
Accepted:
Published online:
Eknath Ghate 1; Mihir Sheth 1
@article{CRMATH_2020__358_5_627_0, 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}, }
TY - JOUR AU - Eknath Ghate AU - Mihir Sheth TI - On non-admissible irreducible modulo $p$ representations of $\protect \mathrm{GL}_{2}(\protect \mathbb{Q}_{p^{2}})$ JO - Comptes Rendus. Mathématique PY - 2020 SP - 627 EP - 632 VL - 358 IS - 5 PB - Académie des sciences, Paris DO - 10.5802/crmath.85 LA - en ID - CRMATH_2020__358_5_627_0 ER -
%0 Journal Article %A Eknath Ghate %A Mihir Sheth %T On non-admissible irreducible modulo $p$ representations of $\protect \mathrm{GL}_{2}(\protect \mathbb{Q}_{p^{2}})$ %J Comptes Rendus. Mathématique %D 2020 %P 627-632 %V 358 %N 5 %I Académie des sciences, Paris %R 10.5802/crmath.85 %G en %F CRMATH_2020__358_5_627_0
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/
[1] Questions on mod representations of reductive -adic groups (2017) (https://arxiv.org/abs/1703.02063)
[2] Central characters for smooth irreducible modular representations of , Rend. Semin. Mat. Univ. Padova, Volume 128 (2012), pp. 1-6 | DOI | MR | Zbl
[3] All reductive p-adic groups are of type I, Funkts. Anal. Prilozh., Volume 8 (1974) no. 2, pp. 3-6 | MR
[4] Representations of Galois and of in characteristic (2007) (Lecture notes of a graduate course at Columbia University)
[5] Towards a modulo Langlands correspondence for , Memoirs of the American Mathematical Society, 216, American Mathematical Society, 2012 | MR | Zbl
[6] Harmonic analysis on reductive p-adic groups. Notes by G. van Dijk, Lecture Notes in Mathematics, 162, Springer, 1970 | Zbl
[7] Representations of a -adic group in characteristic , Representations of reductive groups (Proceedings of Symposia in Pure Mathematics), Volume 101, American Mathematical Society, 2019, pp. 171-210 | DOI | MR
[8] Sur les représentations des groupes réductifs -adiques, C. R. Math. Acad. Sci. Paris, Volume 280 (1975), pp. 1271-1272 | Zbl
[9] On some non-admissible smooth representations of , Math. Res. Lett., Volume 26 (2019) no. 6, pp. 1747-1758 | MR
[10] Coefficient systems and supersingular representations of , Mémoires de la Société Mathématique de France, 99, Société Mathématique de France, 2004 | Numdam | MR | Zbl
[11] Sur la présentation des représentations supersingulières de , J. Reine Angew. Math., Volume 704 (2015), pp. 187-208 | MR | Zbl
[12] Représentations -modulaires d’un groupe réductif -adique avec , Progress in Mathematics, 137, Birkhäuser, 1996 | Zbl
Cited by Sources:
Comments - Policy