Twisted loop groups and their affine flag varieties
By Georgios Pappas, Michael Rapoport. 2006
281 citations recorded by the source corpus.
We develop a theory of affine flag varieties and of their Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field. This can be viewed as a generalization of the theory of affine flag varieties for loop groups to a �twisted case�; a consequence of our results is that our construction also includes the flag varieties for Kac�Moody Lie algebras of affine type. We also give a coherence conjecture on the dimensions of the spaces of global sections of the natural ample line bundles on the partial flag varieties attached to a fixed group over k((t)) and some applications to local models of Shimura varieties
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e3896c6a5ee01795603035321eeba9da7a53dc57
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In Geometry and Topology
- Xinwen Zhu
- Georgios Pappas
- E. Viehmann
- Michael Rapoport
- Xuhua He
- Timo Richarz
- Laurent Fargues
- Peter Scholze
In Mathematical Physics
- Xinwen Zhu
- Georgios Pappas
- E. Viehmann
- Michael Rapoport
- Xuhua He
- Timo Richarz
- Peter Scholze
- Laurent Fargues
Citations in the corpus
- The supersingular locus of the Shimura variety for GU(1,n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {GU} (2013, background): “The relation between L and the Bruhat-Tits simplicial complex is discussed in [20], §4, in the cases where C is split, comp.”
- Geometrization of the local Langlands correspondence: an overview (2016, background): “The BdR-affine Grassmanian: definition.”
- Local models of Shimura varieties and a conjecture of Kottwitz (2011, methodology): “The main ingredients in the proof of this theorem are results of [16, 47] on the structure of Schubert varieties in affine flag varieties and the coherence conjecture of [47] which was shown by the second-named author in [74].”
- The Newton stratification on deformations of local G-shtukas (2008, background): “Moreover [42] present a generalization of results and proofs to twisted a‰ne flag varieties over Fq.”