formal neighbourhood in nLab

Contents

Contents

Idea

A formal neighbourhood is a neighbourhood in formal geometry, hence an “infinitesimal neighbourhood”. Also called a formal completion or formal disk, see there for more.

Examples

• The formal spectrum of the completion of a commutative ring in the II-adic topology for a maximal ideal II is the formal neighbourhood of the point corresponding to that ideal in the spectrum of a commutative ring.

• perturbative quantum field theory (in particular realized as formal deformation quantization) describes the infinitesimal neighbourhood of classical free field theory in the space of all quantum field theories.