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Published in:
2020 | OriginalPaper | Chapter
5. The Nullstellensatz
Author : Daniel Coray
Published in: Notes on Geometry and Arithmetic
Publisher: Springer International Publishing
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Abstract
Hilbert’s Zeros Theorem plays an essential role in algebraic geometry. It allows one to better define morphisms, as the Nullstellensatz implies that the affine algebraic k-varieties form a category equivalent to that of reduced k-algebras of finite type. The most important consequence is the unity of algebra and geometry. Since the field k is arbitrary, this leads to numerous arithmetic applications.