Geodesic
On the algebraic K-theory of some homogeneous varieties
Documenta mathematica, Tome 17 (2012), pp. 167-193
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The K-theory of inner twisted forms of homogeneous varieties G/H with connected reductive algebraic groups H⊂G of the same rank is computed. We provide an explicit isomorphism with the K-theory of certain central simple algebras associated to the considered variety, as a consequence one has that K0​(G/H) is a free abelian group of rank [W(G):W(H)]. The result is used for the computation of the K-theory of some affine homogeneous varieties including an octonionic projective plane and quaternionic projective spaces.
DOI : 10.4171/dm/365
Classification : 14M17, 19E08
Mots-clés : K-theory, central simple algebras, affine homogeneous varieties 
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     author = {Alexey Ananyevskiy},
     title = {On the algebraic {K-theory} of some homogeneous varieties},
     journal = {Documenta mathematica},
     pages = {167--193},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/365},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/365/}
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Alexey Ananyevskiy. On the algebraic K-theory of some homogeneous varieties. Documenta mathematica, Tome 17 (2012), pp. 167-193. doi: 10.4171/dm/365

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