$p$-adic non-abelian Hodge theory for curves via moduli stacks

Ben Heuer, Daxin Xu

For a smooth projective curve $X$ over ${\mathbb{C}}_p$ and any reductive group $G$, we show that the moduli stack of $G$-Higgs bundles on $X$ is a twist of the moduli stack of v-topo…