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Introduction to Algebraic Geometry, Part 1

By Churchill, R.C.

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Book Id: WPLBN0003761721
Format Type: PDF eBook :
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Reproduction Date: 2015

Title: Introduction to Algebraic Geometry, Part 1  
Author: Churchill, R.C.
Language: English
Subject: Programming, Mathematics, Geometry
Collections: Technical Books Center
Publication Date:
Publisher: Department of Mathematics


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Churchill, R. (2007). Introduction to Algebraic Geometry, Part 1. Retrieved from

Description: It is hoped that this note will assist students in untangling the morass: they approach the subject from what could cynically be described as a rather narrow perspective, but they contain far more than the usual amount of detail and they include simple examples illustrating how algebraic geometers would work within this limited context.

Table of Contents
TOC : Part I - Basics - 1. Motivation: Fermat's Last Theorem as a Geometry Problem - 2. Classical A±ne Algebraic Geometry - 3. The Ring-Theoretic Approach - 4. The Topological Approach - 5. The Contemporary Combined Approach - 6. Viewing an Algebraic Set V within Spec(AB[V]) - 7. Maximal Ideals - 8. A Generalization of Affne Algebraic Sets - Part II - Topological Considerations - 9. Zariski Closures - 10. Irreducible Spaces - 11. Noetherian Spaces - 12. Closed Points - 13. An Application of the Prime Spectrum - The In¯nitude of Primes - 14. Specializations and Generic Points - 15. Compactness - 16. Connectedness - 17. Tres Dense Subspaces - Part III - Algebraic Considerations - 18. The Weak Nullstellensatz - 19. The Nullstellensatz - 20. Localization - 21. Finishing Touches - Appendix: Schemes - Notes and Comments - References.


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