Mennicke symbols, $K$-cohomology and a Bass-Kubota theorem
Résumé
If $ A$ is a smooth algebra of dimension $ d\geq 3$ over a perfect field $ k$ of characteristic different from $ 2$, then we show that the universal Mennicke symbol $ MS_{d+1}(A)$ is isomorphic to the $ K$-cohomology group $ H^d(A,K_{d+1})$. We then prove an analogue of the Bass-Kubota theorem for smooth affine surfaces over the algebraic closure of a finite field.