Kirill Zainoulline: On Grothendieck's Conjecture about Principal Homogeneous Spaces for Some Classical Algebraic Groups

kirill@pdmi.ras.ru

Submission: 1999, July 18

In the present paper we investigate the question about the injectivity of the map \$\f(R) \ra \f(K)\$ induced by the canonical inclusion of a local regular ring of geometric type \$R\$ to its field of fractions \$K\$ for a homotopy invariant functor \$\f\$ with transfers satisfying some additional properties. As an application we get the proof of Special Unitary Case of Grothendieck's conjecture about principal homogeneous spaces and some other interesting examples.

1991 Mathematics Subject Classification: 13H05, 14M17

Keywords and Phrases: Azumaya algebra, principal homogeneous space, transfer

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