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arXiv · 0907.2892

Pseudo Algebraically Closed Extensions

Lior Bary-Soroker
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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.

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Lior Bary-Soroker. 2009-07-16. Pseudo Algebraically Closed Extensions. https://arxiv.org/abs/0907.2892

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