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

Alexander Borisov·Mark Sapir
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Abstract

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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Alexander Borisov, Mark Sapir. 2003-09-06. Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms. https://doi.org/10.1007/s00222-004-0411-2

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