Birkhoff's Theorem from a geometric perspective: A simple example
From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2016-02-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | http://www.cgasa.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdf |
| Summary: | From Hilbert's theorem of zeroes, and from Noether's ideal theory, Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces) by the following method, known as Isbell conjugacy. |
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| ISSN: | 2345-5853 2345-5861 |