×

zbMATH — the first resource for mathematics

On the Hodge-Newton decomposition for split groups. (English) Zbl 1074.14016
Summary: The main purpose of this paper is to prove a group-theoretic generalization of a theorem of N. M. Katz on isocrystals [Astérisque 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 M. Rapoport and 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 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.

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
22E50 Representations of Lie and linear algebraic groups over local fields
20G25 Linear algebraic groups over local fields and their integers
PDF BibTeX XML Cite
Full Text: DOI arXiv