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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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
2018.
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| Series: | Memoirs of the American Mathematical Society Ser.
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| Subjects: | |
| Online Access: |
Full text (Wentworth users only) |
| Local Note: | ProQuest Ebook Central |
MARC
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| 100 | 1 | |a Écon, Olivier. | |
| 245 | 1 | 0 | |a Algebraic Overline{ Mathbb{Q}}-Groups As Abstract Groups. |
| 260 | |a Providence : |b American Mathematical Society, |c 2018. | ||
| 300 | |a 1 online resource (112 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v. 255 | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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 groups H(K) and G(K) are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic overline{ mathbb Q} -groups G and H, the elementary equivalence of the pure groups G(K) and H(K) implies that they are abstractly isomorphic. In the final section, the author appli. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Algebra. | |
| 650 | 0 | |a Finite groups. | |
| 650 | 0 | |a Isomorphisms (Mathematics) | |
| 650 | 7 | |a algebra. |2 aat | |
| 776 | 0 | 8 | |i Print version: |a Écon, Olivier. |t Algebraic Overline{ Mathbb{Q}}-Groups As Abstract Groups. |d Providence : American Mathematical Society, ©2018 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 852 | |b Ebooks |h ProQuest | ||
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