Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms

Details Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms

2003-09-06

arxiv.org/abs/math/0309121v1

Mathematics

Group Theory

18 pages

Scientific paper

10.1007/s00222-004-0411-2

We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space.

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