3 problems

Genus finiteness conjecture. The set ${\bf gen}(G)$ is finite.

Let $G$ be an absolutely almost simple group over a finitely generated field $k$, with characteristic of $k$ prime to the order of the Weyl group of $G$. For a field extension…

Let $K$ be a field. For an absolutely almost simple simply connected algebraic $K$-group $G$, write $\mathbf{gen}_K(G)$ for its genus, the set of $K$-isomorphism classes of $K$-for…