= Cyclic formal quotient of the infinite toric chain
{title2=$\widehat X/\langle i\mapsto i+m\rangle$}
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 $(t,q)\mapsto(q^mt,q)$. For $m\geq3$, 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
Back to article page
