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

1999/02/23 by Kirill Zainoulline
Mathematics · #math.AG #math.AC #math.GR #math.KT #math.RA

paper · pdf

published as St.Petersburg Math. J. 12(1), 2001 · AMS-TeX v2.1, 28 pages

arxiv created 1999/02/23 · arxiv updated 2009/11/30

Abstract

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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