Theory of specialisations
<p>This thesis aims to develop a theory of specialisations for Zariski structures. The main question this thesis is centred around is when is a specialisation is κ-universal?</p> <p>In Chapter 3 we look at the case of algebraically closed fields and Zariski structures definable in...
| প্রধান লেখক: | |
|---|---|
| অন্যান্য লেখক: | |
| বিন্যাস: | গবেষণাপত্র |
| ভাষা: | English |
| প্রকাশিত: |
2017
|
| বিষয়গুলি: |
| সংক্ষিপ্ত: | <p>This thesis aims to develop a theory of specialisations for Zariski structures. The main question this thesis is centred around is when is a specialisation is κ-universal?</p>
<p>In Chapter 3 we look at the case of algebraically closed fields and Zariski structures definable in these. We show that any specialisation of an algebraically closed field defines a residue map of a valuation ring, and moreover we show that any residue map induces a κ-universal specialisation whenever the algebraically closed field is κ-saturated over the residue field.</p>
<p>In Chapters 4 and 5 we look at the κ-universal specialisations of finite and infinite covers of Zariski structures. Under some natural assumptions we show that a specialisation of a cover of a Zariski structure is κ-universal if and only if it extends a κ-universal specialisation of a base Zariski structures and satisfies a simple axiom.</p>
|
|---|