an:01917727
Zbl 1074.14016
Kottwitz, Robert E.
On the Hodge-Newton decomposition for split groups
EN
Int. Math. Res. Not. 2003, No. 26, 1433-1447 (2003).
00094605
2003
j
14F30 22E50 20G25
Summary: The main purpose of this paper is to prove a group-theoretic generalization of a theorem of \textit{N. M. Katz} on isocrystals [Ast??risque 63, 113--164 (1979; Zbl 0426.14007)]. Along the way, we re-prove the group-theoretic generalization of Mazur's inequality for isocrystals due to \textit{M. Rapoport} and \textit{M. Richartz} [Compos. Math. 103, 153--181 (1996; Zbl 0874.14008)], and generalize, from split groups to unramified groups, a result from the author and \textit{M. Rapoport} [Comment. Math. Helv. 78, No.1, 153--184 (2003; Zbl 1126.14023)] which determines when the affine Deligne-Lusztig subset \(X^G_{\mu(b)}\) of \(G(L)/G({\mathcal O}_L)\) is nonempty.
Zbl 0426.14007; Zbl 0874.14008; Zbl 1126.14023