On algebraic closure in pseudofinite fields
Logic
2012-01-16 v3
Abstract
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory of pseudo-finite fields we show that algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.
Cite
@article{arxiv.0909.2189,
title = {On algebraic closure in pseudofinite fields},
author = {Özlem Beyarslan and Ehud Hrushovski},
journal= {arXiv preprint arXiv:0909.2189},
year = {2012}
}
Comments
9pp, to appear in JSL. Several corrections in new version; Remark (ii) replaced by Example 11 and Remark 12. Thanks to referee for two very useful reports