Index
New knowls for Galois Extensions and Bundles
The new definitions and bridge results added while knowlifying the Galois Extensions and Bundles conversation.
Core idea
This temporary index lists every knowl added for the conversation. Click any term to expand it in place.
Scheme and sheaf foundations
- Terminal object
- Sheaf
- Sheaf of groups
- Stalk
- Structure sheaf
- Locally ringed space
- Direct image of a sheaf
- Morphism of sheaves
- Morphism of locally ringed spaces
- Affine scheme
- Scheme
- Morphism of schemes
- Scheme over a base
- Fiber product of schemes
- Diagonal morphism
- Base change
- Connected scheme
Étale and site foundations
- Grothendieck topology
- Site
- Sieve on an object
- Covering family in a site
- Finite morphism
- Locally of finite type
- Locally of finite presentation
- Flat morphism
- Relative Kähler differentials
- Unramified morphism
- Étale morphism
- Finite étale morphism
- Étale topology
- Small étale site
- Local diffeomorphism
Torsors and Galois bridges
- Group scheme
- Constant finite group scheme
- -torsor on a site
- Torsor condition
- Finite étale algebra
- Finite Galois algebra
- Galois tensor-product identity
- Galois extension as an étale torsor
Standard examples and points
- Algebraically closed field
- Affine line
- Affine -space
- Projective space
- Proj of a graded ring
- Irreducible space
- Generic point
- Closed point
Pre-existing knowls reused by the transcript
The complete glossary also reuses the following existing definitions rather than duplicating them:
- Field theory: Galois extension, Galois group, field extension, separable extension, and field automorphism.
- Rings and spectra: field, commutative ring, ring homomorphism, ideal, prime ideal, maximal ideal, polynomial ring, prime spectrum, Zariski topology, local ring, and localization.
- Algebra and groups: algebra over a ring, tensor product of algebras, group, and group action.
- Categories and topology: category, object, morphism, isomorphism, contravariant functor, topological space, open cover, open set, and closed set.
- Supporting notions: fiber, local trivialization, function, and integers.