Cyclic formal quotient of the infinite toric chain ($\hat{X}/⟨i\mapsto i+m⟩$)

The lattice shear $(a,b)\mapsto (a+mb,b)$ shifts the chain charts by $m$ and preserves $q$. On the dense torus it acts as $(t,q)\mapsto (q^{m}t,q)$. For $m\ge 3$, translates of each chart of the formal completion of a scheme along $q=0$ are disjoint. Glue $m$ representative formal charts cyclically by the adjacent-chart formulas to obtain a formal scheme quotient. The two branch opens of each chart are disjoint because $D(x_i)\cap D(y_i)=D(q)$ is empty on the formal support. The quotient fibre is an $m$-gon of projective lines, and the quotient map is locally an isomorphism on each translated chart. Invariant morphisms descend uniquely through this gluing.

// Target: ringed-space.bigb