Elementary equivalence of Chevalley groups over fields

Abstract

It is proved that (elementary) Chevalley groups $G_{\pi }(\Phi ,K)$ and $G_{{\pi }^{\prime }}({\Phi }^{\prime },K^{\prime })$ (or $E_{\pi }(\Phi ,K)$ and $E_{{\pi }^{\prime }}({\Phi }^{\prime },K^{\prime }))$ over infinite fields $K$ and $K^{\prime }$ of characteristics $\ne 2$, with weight lattices $\Lambda$ and ${\Lambda }^{\prime }$, respectively, are elementarily equivalent if and only if the root systems $\Phi$ and ${\Phi }^{\prime }$ are isomorphic, the fields $K$ and $K^{\prime }$ are elementarily equivalent, the lattices $\Lambda$ and ${\Lambda }^{\prime }$ coincide.

55 pages