Zariski Geometries

Erscheinungsjahr 2010
ISBN: 978-0-521-73560-5
Verlag: Cambridge University Press

Buch, Englisch, Band 360, 224 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 335 g

Reihe: London Mathematical Society Lecture Note Series

• Contains survey material as well as detailed mathematical proofs
• Assumes no specialist background in logic
• Over 50 exercises help the reader test their understanding of the material
This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Ist logical approach helps us understand why algebraic geometry is so fundamental throughout mathematics and why the extension to noncommutative geometry, which has been forced by recent developments in quantum physics, is both natural and necessary. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.

Autoren/Hrsg.

Zilber, Boris

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

1. Introduction
2. Topological structures
3. Noetherian Zariski structures
4. Classification results
5. Non-classical Zariski geometries
6. Analytic Zariski geometries
A. Basic model theory
B. Geometric stability theory
References
Index.

Über Autor(innen)

Zilber, Boris
Boris Zilber is Professor of Mathematical Logic in the Mathematical Institute at the University of Oxford.