, Volume 85, Issue 1-3, pp 203-262

Groups definable in local fields and pseudo-finite fields

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Abstract

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.

Both authors supported by NSF grants.