English

On motivic decompositions arising from the method of Bialynicki-Birula

Algebraic Geometry 2009-11-10 v3 K-Theory and Homology

Abstract

Recently, V. Chernousov, S. Gille and A. Merkurjev have obtained a decomposition of the motive of an isotropic smooth projective homogeneous variety analogous to the Bruhat decomposition. Using the method of Bialynicki-Birula, I generalize this decomposition to the case of a (possibly anisotropic) smooth projective variety homogeneous under the action of an isotropic reductive group. This answers a question of N. Karpenko.

Keywords

Cite

@article{arxiv.math/0407305,
  title  = {On motivic decompositions arising from the method of Bialynicki-Birula},
  author = {Patrick Brosnan},
  journal= {arXiv preprint arXiv:math/0407305},
  year   = {2009}
}

Comments

Vastly improved with (1) references to important previous work on the subject by S. del Bano, (2) an explicit combinatorial description of the decomposition of projective homogeneous varieties in terms of reflection groups and (3) an illustrative example