Trivial Witt groups of flag varieties

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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https://hal-univ-artois.archives-ouvertes.fr/hal-00579798
Contributor : Baptiste Calmès <>
Submitted on : Friday, March 25, 2011 - 7:39:12 AM
Last modification on : Wednesday, July 27, 2016 - 2:48:48 PM

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  • HAL Id : hal-00579798, version 1
  • ARXIV : 1103.4412

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Baptiste Calmès, Jean Fasel. Trivial Witt groups of flag varieties. 2011. ⟨hal-00579798⟩

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