nLab
locally ringed topological space

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Geometry

Contents

Definition

A locally ringed space is a ringed space (X,𝒪)(X,\mathcal{O}) such that the stalks of the structure sheaf 𝒪\mathcal{O} are local rings.

A morphism of locally ringed space is a morphism of ringed spaces (f,f ):(X,𝒪 X)(Y,𝒪 Y)(f,f^\sharp):(X,\mathcal{O}_X)\to (Y,\mathcal{O}_Y), where f:XYf:X\to Y, such that the comorphism f :𝒪 Yf *𝒪 Xf^\sharp:\mathcal{O}_Y\to f_*\mathcal{O}_X is a morphism of local rings (that is, a map of rings which respects the maximal ideal).

References

Revised on November 22, 2013 03:30:49 by Urs Schreiber (77.251.114.72)