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This is a tentative and preliminary version of these lecture notes and should
Lecture Notes for Math 615, Winter, 2019
Prerequisite material:
Lecture Notes for Math 614, Fall, 2017
References for tight closure:
Tight closure and characteristic p methods
Fundamentals of tight closure theory
Reference for multiplicities, Tor, spectral sequences, and Koszul homology:
Lectures on Commutative Algebra II
Supplements:
Categories and functors, the Zariski topology, and the functor Spec
Integral extensions and integral dependence
Hilbert functions and Hilbert polynomials
Noether normalization and Hilbert's Nullstellensatz
Dimension theory and systems of parameters
Formal power series rings, inverse limits, and I-adic completions of rings
The local nature of an element of a ring or module
Exact sequences with a flat cokernel and a sketch of properties of Tor
Regular rings and finite projective resolutions
The structure theory of complete local rings
not be used as a reference. Some of the material covered will change from what is here.
Problem sets: 1
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5
Solutions: 1
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