Spring 2024
Anders Buch
Course Description:
Commutative algebra provides the basic toolbox in a number of fields including number theory, invariant theory, and algebraic geometry. This course will be an introduction to the subject which mostly focuses on applications to algebraic geometry. The course will emphasize the viewpoint that a commutative ring corresponds to a geometric space. Furthermore, the geometric properties of this space, like its dimension and singularities, are reflected by the algebraic properties of the ring. The course will introduce basic notions such as localization, primary decomposition, integrality, flatness, and dimension. We will also discuss Groebner bases which make it possible to automatically compute solutions to many problems in algebraic geometry on a computer.
Text:
David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer, GTM 150, 1995
Prereq:
640:551/640:552 or equivalent