Birkhoff's Theorem from a geometric perspective: A simple example
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Abstract:
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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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 example that illustrates some of the aspects of this relationship. the dualization from algebra to geometr...
full textBirkhoff’s Theorem from a geometric perspective: A simple example
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full textbirkhoff'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 example that illustrates some of the aspects of this relationship. the dualization from algebra ...
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Journal title
volume 4 issue 1
pages 1- 8
publication date 2016-02-01
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