Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms
نویسندگان
چکیده
منابع مشابه
Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms
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 af...
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This paper is a continuation of paper [1] where we proved that for every linear finitely generated group G and any injective endomorphism φ of G, the mapping torus of φ is residually finite. The mapping torus of φ is the following ascending HNN extension of G: HNNφ (G) = 〈G, t | txt−1 = φ(x)〉 where x runs over a (finite) generating set of G. Probably, the most important mapping tori are mapping...
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Almost all of the general facts about abelian varieties which we use without comment or refer to as "well known" are due to WEIL, and the references for them are [12] and [3]. Let k be a field, k its algebraic closure, and A an abelian variety defined over k, of dimension g. For each integer m > 1, let A m denote the group of elements aeA(k) such that ma=O. Let l be a prime number different fro...
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Proof. It is well-known that the kernels of the powers of φ stabilize (see for example [3]), that is, there exists k > 0 such that ker(φ) = ker(φ) for all n ≥ k. (This easily follows from the stabilization of ranks of the free groups φ(F ) and from Hopficity of finitely generated free groups.) Put N = ker(φ). Then φ factors through to an injective endomorphism φ : F/N → F/N . The group F/N is i...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2004
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-004-0411-2