Inventiones mathematicae

, Volume 160, Issue 2, pp 341–356

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


DOI: 10.1007/s00222-004-0411-2

Cite this article as:
Borisov, A. & Sapir, M. Invent. math. (2005) 160: 341. doi: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.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA