Cohomological Invariants of Simply Connected Groups of Rank 3

Abstract

Let G be a linear algebraic group defined over a field F . One can define an equivalence relation (called R-equivalence) on the group GF‘ of points over F as follows (cf. [4, 9, 14]). Two points g0; g1 ∈ GF‘ are R-equivalent, if there is a rational morphism f x 1 F → G of algebraic varieties over F defined at points 0 and 1 such that f 0‘ = g0 and f 1‘ = g1. The group of R-equivalence classes is denoted by GF‘/R. For example, if G = SL1A‘ is the special linear group of a central simple F-algebra A, then the group of R-equivalence classes GF‘/R is equal to the reduced Whitehead group in algebraic K-theory (cf. [27])