Trivial Witt groups of flag varieties

Details Trivial Witt groups of flag varieties Trivial Witt groups of flag varieties

2011-03-22

arxiv.org/abs/1103.4412v2

Journal of Pure and Applied Algebra, 216 (2012), issue 2, p. 404-406

Mathematics

Algebraic Geometry

3 pages, 1 figure

Scientific paper

10.1016/j.jpaa.2011.07.004

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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