Chernousov–Rapinchuk finiteness conjecture for forms of algebraic groups

Let $K=k(C)$ be the function field of a smooth affine geometrically integral curve over a field $k$, and let $V$ be the set of discrete valuations associated with the closed points of $C$. Let $G$ be an absolutely almost simple simply connected algebraic $K$-group, and let $m$ be the order of the automorphism group of its root system. Assume that $\operatorname{char} k$ is prime to $m$ and that $k$ satisfies $(F_m')$. A $K$-form of $G$ is said to have good reduction at $v\in V$ when it has good reduction at the valuation $v$. Chernousov–Rapinchuk finiteness conjecture. The set of $K$-isomorphism classes of $K$-forms of $G$ that have good reduction at all $v\in V$ is finite. This conjecture extends known finiteness results for spinor groups and special unitary groups to all absolutely almost simple simply connected algebraic groups under the stated assumptions; its general validity remains open.