Select any concept, construction junction, or annotated relation by pointer, touch, search, or keyboard.

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

Canonical static concept record

Scheme over a base

Open this concept in the interactive graph Read the Markdown equivalent

Summary

A scheme $X$ equipped with a specified morphism to a base scheme $S$ .

Record metadata

Canonical name: Scheme over a base
Concept ID: scheme_over_base
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Algebraic geometry
Domains: Algebraic geometry, Category theory
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

scheme $X$
base scheme $S$

Data

structure morphism $X\to S$

Notes

This is the object-level notion of an $S$ -scheme.

Concept sources

Wikipedia — Scheme (mathematics) — Scheme (mathematics) · expository · source ID wp-scheme
Stacks Project — Schemes — Schemes · reference · source ID stacks-scheme
Stacks Project — Projective morphisms — Projective morphisms · reference · source ID stacks-projective-morphisms
Stacks Project — Schemes (PDF) — Schemes (PDF) · reference text · source ID stacks-schemes-text

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Scheme Scheme over a base

Permalink to relation

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

Relation ID: scheme_to_scheme_over_base
Relation type: Add data add-data
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + base and structure morphism

Authored explanation

Choose a base scheme $S$ and a morphism $X\to S$ .

How to interpret this relation type

Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

Relation sources

Stacks Project — Schemes — Schemes · reference · source ID stacks-scheme
Stacks Project — Projective morphisms — Projective morphisms · reference · source ID stacks-projective-morphisms
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.