Algebraic Q-groups as abstract groups / Olivier Fr©♭con.
| Author/creator | Fr©♭con, Olivier, 1974- |
| Format | Electronic |
| Publication Info | Providence, RI, USA : American Mathematical Society, [2018] |
| Description | v, 99 pages ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Supplemental Content | Full text available from Memoirs of the American Mathematical Society |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; Volume 255, number 1219 |
| Contents | Background material -- Expanded pure groups -- Unipotent groups over Q and definable linearity -- Definably affine groups -- Tori in expanded pure groups -- The definably linear quotients of an ACF-group -- The group DG and the main theorem for K = Q -- The main theorem for K = Q -- Bi-interpretability and standard isomorphisms. |
| Abstract | "We analyze the abstract structure of algebraic groups over an algebraically closed field K. For K of characteristic zero and G a given connected affine algebraic Q-group, the main theorem describes all the affine algebraic 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 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 chapter, we apply our results to characterize the connected algebraic groups all of whose abstract automorphisms are standard, when K is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited"-- Provided by publisher. |
| General note | "September 2018 . Volume 255 . Number 1219 (second of 7 numbers)." |
| Bibliography note | Includes bibliographical references (pages 95-96) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2018040526 |
| ISBN | 9781470429232 (pbk. : alk. paper) |
| ISBN | 1470429233 (pbk. : alk. paper) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |