The Batyrev-Manin conjecture for DM stacks II

This is a sequel to a paper by the authors. We formulate a prototype of a Batyrev-Manin type conjecture for DM stacks in positive characteristic with emphasis on the wild case. The key to doing so is the notion of sectoroids, which plays a role similar to the role played by sectors in characteristic zero. We also check some compatibilities of the proposed prototype and see how it reduces to special cases. In the course of formulating the prototype, we introduce a new type of height functions, which is more general and flexible than the one we considered in the preceding paper. Examples of this new height function include discriminants of torsors, minimal discriminants and conductors of elliptic curves in characteristic three. In appendices, we generalize construction of a moduli stack by Tonini-Yasuda and construct a morphism between stacks of twisted arcs. These results are closely related to the main text, but also of independent interest.