Twisted Witt Groups of Flag Varieties
Abstract
Calm\`es 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.
Cite
@article{arxiv.1305.6492,
title = {Twisted Witt Groups of Flag Varieties},
author = {Marcus Zibrowius},
journal= {arXiv preprint arXiv:1305.6492},
year = {2015}
}
Comments
inverse Cartan coefficients for E_7 in Figures 1, 2 and 3 corrected; related mistake in the marking scheme for diagrams of type E_n corrected; many minor corrections and clarifications; more examples