普通型复合旗簇的KO-理论
KO-theory of complex flag varieties of ordinary type
摘要：
我们计算每个普通型复旗流形的拓扑Witt群，从而计算这些流形的KO-群的有趣（即挠）部分。等价地，我们计算特征不为2的代数闭域上的每个普通型旗簇的巴耳末维特群。我们的计算是基于Zibrowius开发的方法。对于A、B和C型，我们不仅得到了分次Witt环的加法结构的完整刻画，而且得到了分次Witt环的乘法结构的完整刻画。
英文摘要：
We compute the topological Witt groups of every complex flag manifold of ordinary type, and thus the interesting (i.e. torsion) part of the KO-groups of these manifolds. Equivalently, we compute Balmer's Witt groups of each flag variety of ordinary type over an algebraically closed field of characteristic not two. Our computation is based on an approach developed by Zibrowius. For types A, B and C, we obtain a full description not only of the additive but also of the multiplicative structure of the graded Witt rings.
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