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Algebraic Overline{ Mathbb{Q}}-Groups As Abstract Groups.
The author analyzes the abstract structure of algebraic groups over an algebraically closed field K. For K of characteristic zero and G a given connected affine algebraic \overline{\mathbb Q}-group, the main theorem describes all the affine algebraic \overline{\mathbb Q} -groups H such that the grou...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2018.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; 1.1. Related work; 1.2. The field of definition; 1.3. Overview of the paper; Chapter 2. Background material; 2.1. Groups of finite Morley rank; 2.2. Fundamental theorems; 2.3. Decent tori and pseudo-tori; 2.4. Unipotence; Chapter 3. Expanded pure groups; Chapter 4. Unipotent groups over \ov{\Q} and definable linearity; Chapter 5. Definably affine groups; 5.1. Definition and generalities; 5.2. The subgroup (); 5.3. The subgroup (); Chapter 6. Tori in expanded pure groups; Chapter 7. The definably linear quotients of an -group.
- 7.1. The subgroups () and ()7.2. The nilpotence of (); 7.3. The subgroup () when the ground field is \ov{\Q}; 7.4. The subgroups () and () in positive characteristic; Chapter 8. The group _{ } and the Main Theorem for =\ov{\Q}; Chapter 9. The Main Theorem for `"ov{\Q}; Chapter 10. Bi-interpretability and standard isomorphisms; 10.1. Positive characteristic and bi-interpretability; 10.2. Characteristic zero; Acknowledgements; Bibliography; Index of notations; Index; Back Cover.