On Grothendieck's Conjecture about Principal Homogeneous Spaces for some Classical Algebraic Groups, by Kirill Zainoulline

In the present paper we investigate the question about the injectivity of the map F(R) --> 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 original proof of Special Unitary Case of Grothendieck's conjecture about principal homogeneous spaces and some other interesting examples.

Kirill Zainoulline <kirill@pdmi.ras.ru>