MATH 6340 - Commutative Algebra with Applications in Algebraic Geometry

Irena Peeva, fall 2016.

The lectures will emphasize the connections between Commutative Algebra and Algebraic Geometry. The choice of topics will depend on the interests and background of the audience. Some possible topics: localization, primary decomposition, dimension theory, flatness, completion, integral extensions, Hilbert polynomials, free resolutions, homology and cohomology, complete intersections, Gorenstein rings, Cohen-Macaulay rings and modules.

Prerequisites

A good background in abstract algebra.

Textbooks

• D. Eisenbud, Commutative Algebra, Springer 1994.
• M. Atiyah and I. MacDonald, Introduction to Commutative Algebra, Addison Wesley 1969
• H. Matsumura, Commutative ring theory, Cambridge University Press 1986.