Submission: 2005, Mar 3
Given a characteristic zero field and a dominant morphism of linear algebraic groups with a commutative target one can form a functor from commutative algebras to abelian groups. The functor takes an algebra to the group of points of the target group modulo the group of points of the sourse. It is proved that this functor satisfies a purity theorem for any regular local algebra. Few examples are considered in the very end of the preprint.
2000 Mathematics Subject Classification: 11E72
Keywords and Phrases: classical simple groups, exceptional simple groups, purity theorem, homotopy invariance, norms.
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