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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Borisov, A., Sapir, M. Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms. Invent. math. 160, 341–356 (2005). https://doi.org/10.1007/s00222-004-0411-2
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DOI: https://doi.org/10.1007/s00222-004-0411-2