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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Groups definable in separably closed fields


Authors: E. Bouscaren and F. Delon
Journal: Trans. Amer. Math. Soc. 354 (2002), 945-966
MSC (1991): Primary 03C60, 03C45, 12L12
Published electronically: October 24, 2001
MathSciNet review: 1867366
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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 $L$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02886-0
PII: S 0002-9947(01)02886-0
Keywords: Separably closed fields, groups
Received by editor(s): January 10, 1999
Received by editor(s) in revised form: September 20, 2000
Published electronically: October 24, 2001
Article copyright: © Copyright 2001 American Mathematical Society