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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Groups definable in separably closed fields
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by E. Bouscaren and F. Delon PDF
Trans. Amer. Math. Soc. 354 (2002), 945-966 Request permission

Abstract:

We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field $L$ is definably isomorphic to the group of $L$-rational points of an algebraic group defined over $L$.
References
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Additional Information
  • E. Bouscaren
  • Affiliation: Université Paris 7- CNRS, UFR de Mathématiques, Case 7012, 2 Place Jussieu, 75251 Paris cedex 05, France
  • Email: elibou@logique.jussieu.fr
  • F. Delon
  • Affiliation: Université Paris 7- CNRS, UFR de Mathématiques, Case 7012, 2 Place Jussieu, 75251 Paris cedex 05, France
  • Email: delon@logique.jussieu.fr
  • Received by editor(s): January 10, 1999
  • Received by editor(s) in revised form: September 20, 2000
  • Published electronically: October 24, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 945-966
  • MSC (1991): Primary 03C60, 03C45, 12L12
  • DOI: https://doi.org/10.1090/S0002-9947-01-02886-0
  • MathSciNet review: 1867366