The Buzzard–Diamond–Jarvis conjecture for unitary groups

Gee, Toby¹ ; Liu, Tong² ; Savitt, David³

¹ Department of Mathematics, Imperial College London, London, SW7 2AZ United Kingdom
² Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
³ Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, Arizona 85721-0089

Journal of the American Mathematical Society, Tome 27 (2014) no. 2, pp. 389-435

Résumé

Let $p>2$ be prime. We prove the weight part of Serre’s conjecture for rank two unitary groups for mod $p$ representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of $(\varphi ,\hat {G})$-modules to determine the possible reductions of certain two-dimensional crystalline representations.

Détail

DOI : 10.1090/S0894-0347-2013-00775-4

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