Israel Journal of Mathematics

, Volume 85, Issue 1, pp 203–262

Groups definable in local fields and pseudo-finite fields

Article

DOI: 10.1007/BF02758643

Cite this article as:
Hrushovski, E. & Pillay, A. Israel J. Math. (1994) 85: 203. doi:10.1007/BF02758643

Abstract

Using model-theoretic methods we prove:

Theorem A

If G is a Nash group over the real or p-adic field, then there is a Nash isomorphism between neighbourhoods of the identity of G and of the set of F-rational points of an algebraic group defined over F.

Theorem B

Let G be a connected affine Nash group over ℝ. Then G is Nash isogeneous with the (real) connected component of the set of real points of an algebraic group defined over ℝ.

Theorem C

Let G be a group definable in a pseudo-finite field F. Then G is definably virtually isogeneous with the set of F-rational points of an algebraic group defined over F.

Copyright information

© Hebrew University 1994

Authors and Affiliations

  1. 1.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Department of MathematicsUniversity of Notre DameNotre DameUSA
  4. 4.Department of MathematicsWesleyan UniversityMiddletownUSA