Harder's Tamagawa number conjecture for split semisimple groups

Let $k$ be a finite field, let $X$ be a smooth geometrically connected projective curve over $k$ with function field $K$, and let ${\mathcal G}$ be a semisimple group scheme over $X$, with generic fibre $G$. The group $G$ is split when it admits a split maximal torus over $K$.

Harder's conjecture. If ${\mathcal G}$ is split, the Tamagawa number of $G$ equals the number of connected components of the moduli space of ${\mathcal G}$-torsors on $X$.

The conjecture relates the arithmetic invariant given by the Tamagawa number to the geometry of the moduli space of torsors. The source introduces it as the motivating connection between Tamagawa numbers and Frobenius traces; its resolution status is not specified here.