Twisted loop groups and their affine flag varieties

• Autores: Georgios Pappas, Michael Rapoport
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 1, 2008, págs. 118-198
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.04.006
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• Resumen

  • 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