Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups

Released on by Olivier Frécon
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  • Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups Book Detail

  • Author : Olivier Frécon
  • Release Date : 2018-10-03
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 112
  • ISBN 13 : 1470429233
  • File Size : 58,58 MB
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Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups by Olivier Frécon PDF Summary

Book Description: The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.

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