The profinite polynomial automorphism group

• Stefan Maubach ^[1] ; Abdul Rauf ^[2]
  1. [1] Rotterdam University of Applied Sciences

     Rotterdam University of Applied Sciences

     Países Bajos

     
  2. [2] Jacobs University

     Jacobs University

     Kreisfreie Stadt Bremen, Alemania

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 10 (October 2015), 2015, págs. 4708-4727
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.03.003
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• Resumen

  • We introduce an extension of the (tame) polynomial automorphism group over finite fields: the profinite (tame) polynomial automorphism group, which is obtained by putting a natural topology on the automorphism group. We show that most known candidate non-tame automorphisms are inside the profinite tame polynomial automorphism group, giving another result showing that tame maps are potentially “dense” inside the set of automorphisms. We study the profinite tame automorphism group and show that it is not far from the set of bijections obtained by endomorphisms.