Twisted Witt groups of flag varieties
\textit{B. Calmès} and \textit{J. Fasel} [J. Pure Appl. Algebra 216, No. 2, 404--406 (2012; Zbl 1235.19002)] 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, the author sharpens their result to an if-and-only-if statement. In particular, he shows that the twisted Witt groups vanish in many previously unknown cases. In the non-zero cases, he finds 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.NEWLINENEWLINEThe 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.
scientific article; zbMATH DE number 6334063