## MATH 615, WINTER 2010

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Administrative Matters

These are preliminary versions of these lecture notes and should

not be used as a reference.

Lecture Notes for Math 615, Winter, 2010

Problem sets: 1
2
3
4
5

Solutions: 1 2 3 4 5

Prerequisite material:

Lecture Notes for Math 614, Fall, 2008

Supplements:

Categories and functors, the Zariski topology, and the functor Spec

Integral extensions and integral dependence

Noether normalization and Hilbert's Nullstellensatz

Dimension theory and systems of parameters

Affine algebraic geometry

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