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

2003/09/06 by Alexander Borisov, Mark Sapir · 1 citation
Mathematics · #math.GR #math.AG #msc:20E06 #msc:20E26 #msc:14G15

paper · pdf · doi:10.1007/s00222-004-0411-2

18 pages

arxiv created 2003/09/06 · arxiv updated 2009/12/01

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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