Outer forms of type $A_2$ with infinite genus

By Sergey V. Tikhonov. 2023

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Let $G$ be an absolutely almost simple algebraic group over a field $K$. The genus ${\bf gen}_K(G)$ of $G$ is the set of $K$-isomorphism classes of $K$-forms $G'$ of $G$ that have the same $K$-isomorphism classes of maximal $K$-tori as $G$. We construct an example of outer forms of type $A_2$ with infinite genus.

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