Pseudo Algebraically Closed Extensions
Abstract
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
Cite
@article{arxiv.0907.2892,
title = {Pseudo Algebraically Closed Extensions},
author = {Lior Bary-Soroker},
journal= {arXiv preprint arXiv:0907.2892},
year = {2009}
}
Comments
PhD thesis done at Tel-Aviv University under the supervision of Prof. Dan Haran. The original thesis is written in Hebrew