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Twisted Witt Groups of Flag Varieties

Published online by Cambridge University Press:  17 April 2014

Marcus Zibrowius
Marcus Zibrowius*
Affiliation:
Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germanymarcus.zibrowius@cantab.net
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Abstract

Calmès and Fasel have shown that the twisted Witt groups of split flag varieties vanish in a large number of cases. For flag varieties over algebraically closed fields, we sharpen their result to an if-and-only-if statement. In particular, we show that the twisted Witt groups vanish in many previously unknown cases. In the non-zero cases, we find that the twisted total Witt group forms a free module of rank one over the untwisted total Witt group, up to a difference in grading.

Our proof relies on an identification of the Witt groups of flag varieties with the Tate cohomology groups of their K-groups, whereby the verification of all assertions is eventually reduced to the computation of the (twisted) Tate cohomology of the representation ring of a parabolic subgroup.

Keywords

Witt groupsflag varietieshomogeneous spacesTate cohomologyparabolic subgroupsPrimary: 18F25Secondary: 19G99, 20G05
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 1 , August 2014 , pp. 139 - 184
Copyright
Copyright © ISOPP 2014 

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