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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Ringed space

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Summary

A topological space equipped with a sheaf of rings.

Record metadata

Canonical name: Ringed space
Concept ID: ringed_space
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Algebraic geometry
Domains: Algebraic geometry, Topology, Algebra
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

topological space $X$

Data

sheaf of rings $O_X$

Concept sources

Wikipedia — Ringed space — Ringed space · expository · source ID wp-ringed-space
nLab — Ringed space — Ringed space · reference · source ID nlab-ringed-space
Stacks Project — Ringed spaces — Ringed spaces · reference · source ID stacks-ringed-space

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

space + sheaf of rings(construction junction)Ringed space

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: j_ringed_space__out
Relation type: Combine compatible structures combine-compatible
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: impose compatibility

Authored explanation

Use the same topological space as the base of the sheaf of rings.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Stacks Project — Ringed spaces — Ringed spaces · reference · source ID stacks-ringed-space
nLab — Ringed space — Ringed space · reference · source ID nlab-ringed-space
Wikipedia — Ringed space — Ringed space · expository · source ID wp-ringed-space
Stacks Project — Schemes (PDF) — Schemes (PDF) · reference text · source ID stacks-schemes-text

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Ringed space Locally ringed space

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: e_ringed_locally
Relation type: Impose axiom impose-axiom
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + local stalks

Authored explanation

Require every stalk of the structure sheaf to be a local ring.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Stacks Project — Locally ringed spaces — Locally ringed spaces · reference · source ID stacks-locally-ringed
nLab — Locally ringed space — Locally ringed space · reference · source ID nlab-locally-ringed
Stacks Project — Schemes (PDF) — Schemes (PDF) · reference text · source ID stacks-schemes-text

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Ringed space

Summary

Record metadata

Carrier(s)

Data

Concept sources

Incoming relations (arrows to this concept)

space + sheaf of rings(construction junction)Ringed space

Authored explanation

How to interpret this relation type

Relation sources

Outgoing relations (arrows from this concept)

Ringed space Locally ringed space

Authored explanation

How to interpret this relation type

Relation sources