Formal Completion along a Closed Subset
Formal completion isolates the infinitesimal geometry supported on a chosen closed subset. Read its description by a functor of points and compare it with the affine construction from quotients of the coordinate ring.
Before opening the references
Scheme · Ideal of a Commutative Ring · Representable Functor · Categorical Limit
Where to read
Start here: The Stacks Project — Completion along a closed subset
The Stacks Project Authors · Online reference · English · Free full text
Section 87.14, Lemmas 87.14.1–87.14.2 and Definition 87.14.3
Continue from here
Algebraic Geometry in the library · Preparation and skip guidance