On Grothendieck's Conjecture about Principal Homogeneous Spaces for some Classical Algebraic Groups

Details On Grothendieck's Conjecture about Principal Homogeneous Spaces for some Classical Algebraic Groups On Grothendieck's Conjecture about Principal Homogeneous Spaces for some Classical Algebraic Groups

1999-02-23

arxiv.org/abs/math/9902132v1

St.Petersburg Math. J. 12(1), 2001

Mathematics

Algebraic Geometry

AMS-TeX v2.1, 28 pages

Scientific paper

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.

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