1
Foundational Locale Theory
▶
1.1
Frames and Basic Structure
1.2
Frame Presentations
2
The Zariski Locale from Commutative Rings
▶
2.1
Radical Ideals as a Frame
2.2
Frame Distributivity for Radical Ideals
2.3
Basic Open Sets
2.4
Frame Presentation of the Zariski Locale
3
Functoriality and Ring Homomorphisms
▶
3.1
Functorial Behavior of Spec
3.2
Functorial Properties
4
The Structure Sheaf
▶
4.1
Sheaves on Locales
4.2
The Structure Sheaf on Zariski Locales
5
Schemes as Locally Ringed Locales
▶
5.1
Locally Ringed Locales
5.2
Affine Schemes
5.3
Morphisms of Schemes
5.4
Gluing and General Schemes
6
Basic Properties of Schemes
▶
6.1
Open and Closed Sublocales
6.2
Irreducibility and Primeness
6.3
Irreducible Schemes
Dependency graph
Pointless Schemes
Aarhus AI4Math Workshop 2026
1
Foundational Locale Theory
1.1
Frames and Basic Structure
1.2
Frame Presentations
2
The Zariski Locale from Commutative Rings
2.1
Radical Ideals as a Frame
2.2
Frame Distributivity for Radical Ideals
2.3
Basic Open Sets
2.4
Frame Presentation of the Zariski Locale
3
Functoriality and Ring Homomorphisms
3.1
Functorial Behavior of Spec
3.2
Functorial Properties
4
The Structure Sheaf
4.1
Sheaves on Locales
4.2
The Structure Sheaf on Zariski Locales
5
Schemes as Locally Ringed Locales
5.1
Locally Ringed Locales
5.2
Affine Schemes
5.3
Morphisms of Schemes
5.4
Gluing and General Schemes
6
Basic Properties of Schemes
6.1
Open and Closed Sublocales
6.2
Irreducibility and Primeness
6.3
Irreducible Schemes