On parahoric Hitchin systems over curves

In this paper, we talk about parahoric Hitchin systems over smooth projective curves with the structure group a semisimple simply connected group. We prove the equivalence of parahoric Hitchin systems over the curve with Hitchin systems over a corresponding root stack with a finite cyclic group action determined (up to conjugation) by the parahoric data. And we also show the compatibility of the equivalence with Hitchin maps. We work over an algebraically closed field with a mild assumption of the characteristic.