On the ${\mathbb{A}}^1$-invariance of ${\mathrm{K}}_2$ modeled on linear and even orthogonal groups

Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky

Let $k$ be an arbitrary field. In this paper we show that in the linear case ($\Phi ={\mathsf{A}}_{\ell }$, $\ell \ge 4$) and even orthogonal case ($\Phi ={\mathsf{D}}_{\ell }$, $\ell \ge 7$, $\ma…