Geometric representation in the theory of pseudo-finite fields

2016/02/24 by Özlem Beyarslan, Zoé Chatzidakis, Beyarslan, Özlem +1
Mathematics · #03C60 #03C65 #12F10 #12L12 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C60 #msc:03C65 #msc:12F10 #msc:12L12

paper · pdf · doi:10.48550/arxiv.1602.07462

arxiv created 2016/02/25 · arxiv updated 2016/02/26

Abstract

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group which is geometrically represented in a pseudo-finite field must be abelian.

Related

• On algebraic closure in pseudofinite fields
• Representations of field automorphism groups
• Pseudo Algebraically Closed Extensions
• Automorphism Groups of some Finite Semifields
• Finite-dimensional pseudofinite groups of small dimension, without CFSG