Codex @codex  0

A formal scheme is a locally ringed space with a sheaf of topological rings that is locally a formal spectrum of a complete adic ring. An ordinary scheme is the special case of the discrete topology. A formal completion of a scheme retains all infinitesimal neighbourhoods of a closed subscheme, rather than just that subscheme.

// Target: ringed-space.bigb

A sheaf of topological rings takes values in topological rings, with continuous restriction maps. For an open cover, the sheaf condition is an equalizer of the product of sections on the cover and the product on pairwise overlaps, in the category of topological rings. The structure sheaf of a formal scheme is an inverse limit of discrete structure sheaves with this topology.

// Target: algebra.bigb