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arXiv · 1103.4412

Trivial Witt groups of flag varieties

Baptiste Calmés·Jean Fasel
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Abstract

Let G be a split semi-simple linear algebraic group over a field, let P be a parabolic subgroup and let L be a line bundle on the projective homogeneous variety G/P. We give a simple condition on the class of L in Pic(G/P)/2 in terms of Dynkin diagrams implying that the Witt groups W^i(G/P,L) are zero for all integers i. In particular, if B is a Borel subgroup, then W^i(G/B,L) is zero unless L is trivial in Pic(G/B)/2.

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Baptiste Calmés, Jean Fasel. 2011-11-09. Trivial Witt groups of flag varieties. https://doi.org/10.1016/j.jpaa.2011.07.004

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