From P-Modular to p-Adic Langlands Correspondences for U(1,1)(\mathbbQp2/\mathbbQp) : Deformations in the Non-Supercuspidal Case

Ramla Abdellatif (1) , A. David (2) , B. Romano , H. Wiersema

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 CRISMAT - Laboratoire de cristallographie et sciences des matériaux

This paper surveys what is known about (conjectural) p-adic and p-modular semisimple Langlands correspondences in the non-supercuspidal setting for the unramified quasi-split unitary groupU(1,1)(\mathbbQp2/\mathbbQp). It focuses in particular on the potential of deformation theory to relate these correspondences. \textcopyright 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Domaines: Mathématiques [math]

Ramla Abdellatif, A. David, B. Romano, H. Wiersema. From P-Modular to p-Adic Langlands Correspondences for U(1,1)(\mathbbQp2/\mathbbQp) : Deformations in the Non-Supercuspidal Case. Association for Women in Mathematics Series, 2021, 24, pp.1--38. ⟨10.1007/978-3-030-77700-5_1⟩. ⟨hal-03682200⟩