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作者 Frecon, Olivier (1974-....). Author.
書名 Algebraic Q-groups as abstract groups / Olivier Frecon
出版項 Providence, Rhode Island : AMS, American Mathematical Society
copyright 2018
國際標準書號 9781470429232 (br)
1470429233 (br)
國際標準號碼 9781470429232
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA174.2 F74 2018    在架上    30340200561235
說明 1 vol. (V-99 p.) ; 26 cm
txt rdacontent
n rdamedia
n isbdmedia
系列 Memoirs of the American Mathematical Society, 0065-9266 ; 1219
Memoirs of the American Mathematical Society ; 1219. 0065-9266
附註 Bibliogr. p. 95-96. Index
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
"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
主題 Q-groups
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