  The purpose of the present paper is to develop the theory of (pre-)Tango
structures and (dormant generic) Miura $\mathfrak{g}$-opers (for a semisimple
Lie algebra $\mathfrak{g}$) defined on pointed stable curves in positive
characteristic. A (pre-)Tango structure is a certain line bundle of an
algebraic curve in positive characteristic, which gives some pathological
(relative to zero characteristic) phenomena. In the present paper, we construct
the moduli spaces of (pre-)Tango structures and (dormant generic) Miura
$\mathfrak{g}$-opers respectively, and prove certain properties of them. One of
the main results of the present paper states that there exists a bijective
correspondence between the (pre-)Tango structures (of prescribed monodromy) and
the dormant generic Miura $\mathfrak{s} \mathfrak{l}_2$-opers (of prescribed
exponent). By means of this correspondence, we achieve a detailed understanding
of the moduli stack of (pre-)Tango structures. As an application, we construct
a family of algebraic surfaces in positive characteristic parametrized by a
higher dimensional base space whose fibers are pairwise non-isomorphic and
violate the Kodaira vanishing theorem.
