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

By A. Borisov, Mark V. Sapir. 2003

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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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/29b7b574cc3c83968fa39aeadd5c0a140da857bf