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A note on groups definable in difference fields
Author(s):
Piotr
Kowalski;
A.
Pillay
Journal:
Proc. Amer. Math. Soc.
130
(2002),
205-212.
MSC (2000):
Primary 03C60.
Posted:
May 22, 2001
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Abstract:
We prove that a group definable in a model of  is virtually definably embeddable in an algebraic group. We give an improved proof of the same result for groups definable in differentially closed fields. We also extend to the difference field context results on the unipotence of definable groups on affine spaces.
References:
- 1.
- M. Chalupnik and P. Kowalski, Lazard's theorem for differential algebraic groups and pro-algebraic groups on affine spaces, preprint 1999.
- 2.
- Z. Chatzidakis and E. Hrushovski, Model theory of difference fields, Transactions of AMS, 351 (1999), 2997-3071. MR 2000f:03109
- 3.
- Z. Chatzidakis, E. Hrushovski and Y. Peterzil, The model theory of difference fields II: periodic ideals and the trichotomy theorem in all characteristics, submitted to Proceedings of London Math. Soc.
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- 5.
- E. Hrushovski and A. Pillay, Groups definable in local fields and pseudo-finite fields Israel Journal of Math., 85 (1994), 203-262. MR 95f:12015
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- P. Kowalski and A. Pillay, Pro-algebraic and differential algebraic group structures on affine spaces, American Journal of Mathematics, 1222 (2000), 213-221. CMP 2000:07
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Additional Information:
Piotr
Kowalski
Affiliation:
Department of Mathematics, University of Wroclaw, pl Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Email:
pkowa@math.uni.wroc.pl
A.
Pillay
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email:
pillay@math.uiuc.edu
DOI:
10.1090/S0002-9939-01-06004-X
PII:
S 0002-9939(01)06004-X
Received by editor(s):
April 5, 2000
Received by editor(s) in revised form:
May 16, 2000
Posted:
May 22, 2001
Additional Notes:
The first author was supported by grant KBN 2 PO3A 020 18
The second author was supported by an NSF grant
Communicated by:
Carl G. Jockusch, Jr.
Copyright of article:
Copyright
2001,
American Mathematical Society
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