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arXiv · 1305.6492

Twisted Witt Groups of Flag Varieties

Marcus Zibrowius
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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.

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Marcus Zibrowius. 2014-02-07. Twisted Witt Groups of Flag Varieties. https://doi.org/10.1017/is014003028jkt260

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