Journal
ADVANCES IN MATHEMATICS
Volume 219, Issue 1, Pages 118-198Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2008.04.006
Keywords
loop group; affine Kac-Moody algebra; Schubert variety; Shimura variety
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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. (c) 2008 Elsevier Inc. All rights reserved.
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