14Lxx Algebraic groups
This subtopic studies algebraic groups, including linear algebraic groups, group actions, and the interplay between geometry and group structure.
Specific topics
14L05 Formal groups, $p$-divisible groups
Overview
14L05 studies formal groups, p-divisible groups in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Formal groups, p-divisible groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for formal groups, p-divisible groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L10 Group varieties
Overview
14L10 studies group varieties in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Group varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for group varieties
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L15 Group schemes
Overview
14L15 studies group schemes in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Group schemes (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for group schemes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L17 Affine algebraic groups, hyperalgebra constructions
Overview
14L17 studies affine algebraic groups, hyperalgebra constructions in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Affine algebraic groups, hyperalgebra constructions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for affine algebraic groups, hyperalgebra constructions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L24 Geometric invariant theory
Overview
14L24 studies geometric invariant theory in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Geometric invariant theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for geometric invariant theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L30 Group actions on varieties or schemes (quotients)
Overview
14L30 studies group actions on varieties or schemes (quotients) in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Group actions on varieties or schemes (quotients) (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for group actions on varieties or schemes (quotients)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L35 Classical groups (geometric aspects)
Overview
14L35 studies classical groups (geometric aspects) in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Classical groups (geometric aspects) (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for classical groups (geometric aspects)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L40 Other algebraic groups
Overview
14L40 studies other algebraic groups in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
Other algebraic groups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other algebraic groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks
14L99 None of the above
Overview
14L99 studies none of the above in algebraic groups. It emphasizes geometric and scheme-theoretic group structures together with quotient constructions, invariants, and representation-adjacent phenomena.
Related Wikipedia Page
None of the above (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for none of the above
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Structure theory for algebraic groups and schemes
- Quotients, invariants, and symmetry in algebraic geometry
- Connections to arithmetic groups and representation theory
References
Recommended Textbooks