14Kxx Abelian varieties and complex tori
This subtopic studies abelian varieties and complex tori, examining their geometry, endomorphisms, and deep arithmetic and analytic structure.
Specific topics
14K02 Isogenies and endomorphisms of abelian varieties
Overview
14K02 studies isogenies and endomorphisms of abelian varieties in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Isogenies and endomorphisms of abelian varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for isogenies and endomorphisms of abelian 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K05 Algebraic theory of abelian varieties
Overview
14K05 studies algebraic theory of abelian varieties in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Algebraic theory of abelian varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for algebraic theory of abelian 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K10 Algebraic moduli of abelian varieties, classification
Overview
14K10 studies algebraic moduli of abelian varieties, classification in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Algebraic moduli of abelian varieties, classification (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for algebraic moduli of abelian varieties, classification
- 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K12 Subvarieties of abelian varieties
Overview
14K12 studies subvarieties of abelian varieties in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Subvarieties of abelian varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for subvarieties of abelian 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K15 Arithmetic ground fields for abelian varieties
Overview
14K15 studies arithmetic ground fields for abelian varieties in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Arithmetic ground fields for abelian varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for arithmetic ground fields for abelian 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K20 Analytic theory of abelian varieties; abelian integrals
Overview
14K20 studies analytic theory of abelian varieties; abelian integrals in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Analytic theory of abelian varieties; abelian integrals (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analytic theory of abelian varieties; abelian integrals
- 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K22 Complex multiplication and abelian varieties
Overview
14K22 studies complex multiplication and abelian varieties in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Complex multiplication and abelian varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for complex multiplication and abelian 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K25 Theta functions and abelian varieties
Overview
14K25 studies theta functions and abelian varieties in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Theta functions and abelian varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for theta functions and abelian 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K30 Picard schemes, higher Jacobians
Overview
14K30 studies picard schemes, higher jacobians in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
Related Wikipedia Page
Picard schemes, higher Jacobians (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for picard schemes, higher jacobians
- 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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks
14K99 None of the above
Overview
14K99 studies none of the above in abelian varieties and complex tori. It emphasizes the algebraic and analytic structure of abelian varieties, their moduli, and the arithmetic phenomena encoded by isogenies, theta data, and complex multiplication.
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
- Theory and classification of abelian varieties
- Moduli and arithmetic study of complex tori
- Links to theta functions, Jacobians, and complex multiplication
References
Recommended Textbooks