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Groups definable in separably closed fields
Author(s):
E.
Bouscaren;
F.
Delon
Journal:
Trans. Amer. Math. Soc.
354
(2002),
945-966.
MSC (1991):
Primary 03C60, 03C45, 12L12
Posted:
October 24, 2001
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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  is definably isomorphic to the group of  -rational points of an algebraic group defined over  .
References:
-
- [BoDe]
- E. Bouscaren and F. Delon, Minimal groups in separably closed fields, to appear in the Journal of Symbolic Logic.
- [De 88]
- F. Delon, Idéaux et types sur les corps séparablement clos, Supplément au Bulletin de la SMF, Mémoire 33, Tome 116 (1988). MR 90m:03067
- [De 98]
- F. Delon, Separably closed fields, in Model Theory and Algebraic Geometry, E. Bouscaren (Ed.), Lecture Notes in Mathematics 1696, Springer, 1998. MR 2000a:12011
- [Hu 87]
- J.E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, Springer, 1987. MR 53:633
- [Hr 96]
- E. Hrushovski, The Mordell-Lang conjecture for function fields, Journal AMS 9 (1996), 667-690. MR 97h:11154
- [La 58]
- S. Lang, Introduction to algebraic geometry, Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers, New York, 1958. MR 20:7021
- [Me 94]
- M. Messmer, Groups and fields interpretable in separably closed fields, TAMS 344 (1994), 361-377. MR 95c:03086
- [Me 96]
- M. Messmer, Some model theory of separably closed fields, in Model Theory of Fields, Lecture Notes in Logic 5, Springer, 1996. MR 98m:03075
- [Pi 96]
- A. Pillay, Geometrical Stability Theory, Oxford University Press, 1996. MR 98a:03049
- [Pi 98]
- A. Pillay, Model theory of algebraically closed fields, in Model Theory and Algebraic Geometry, E. Bouscaren (Ed.), Lecture Notes in Mathematics 1696, Springer, 1998. MR 2000f:12008
- [Po 87]
- B. Poizat, Groupes Stables, Nur al-mantiq wal ma'rifah, Villeurbanne, France, 1987. MR 89b:03056
- [Sp 98]
- T.A. Springer, Linear algebraic groups, 2nd edition, Birkhäuser, 1998. MR 99h:20075
- [Wa 97]
- F. Wagner, Stable Groups, London Math. Soc. LNS 240, Cambridge University Press, 1997. MR 99g:20010
- [We 55]
- A. Weil, On algebraic groups of transformations, American Journal of Math. 77 (1955), 355-391. MR 17:533f
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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:
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
Posted:
October 24, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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