Administrative Matters
These are preliminary versions of these lecture notes and should
Lecture Notes for Math 615, Winter, 2010
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
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.
Problem sets: 1
2
3
4
5