Artin–Schreier root stacks

We classify stacky curves in characteristic p>0 with cyclic stabilizers of order p using higher ramification data. This approach replaces the local root stack structure a tame curve, similar to complex orbifold more sensitive called an Artin–Schreier stack, allowing us incorporate this data directly into stack. As application, we compute dimensions Riemann–Roch spaces for some examples positive and suggest program computing modular forms setting.