Algebraic Geometry Codes
Spring 2018
Other notes
Below are my handwritten notes in case you find them useful. These notes are meant for my own use and so they are not complete and don't have a "soul" (unlike, hopefully, the lectures themselves). I'm mostly following Lorenzini's truly marvellous book An Invitation to Arithmetic Geometry and so you can see more details there.
Chapter 0  Why bother?

Goppa codes

What we'll learn (and what will have to wait for the followup course)
Chapter 1  Introduction to algebraic curves
This chapter closely follows Lorenzini 2.12.5.
Chapter 2  Commutative algebra and a tiny tiny bit of Galois theory
But for (1), (3), this chapter is closely follows Lorenzini, Chapter 1 and 2.6
Chapter 3  Algebraic curves continued
This chapter closely follows Lorenzini 2.72.10

Hilbert's basis theorem
Chapter 4  Factorization of ideals
This chapter closely follows Lorenzini 3.13.8

Ramification index, residual degree, and the fundamental equality

Explicit factorization in Dedekind domains obtained via a monic polynomial

Factorization in ArtinSchreier extensions and Kummer extensions

A tiny bit more on Galois theory
Chapter 5  Valuations
This chapter closely follows Lorenzini 4.2,4.6,5.2,5.3,5.6,5.8.

Rings with finite quotients

Absolute values and valuations

Discrete valuation rings
Chapter 6  Projective curves and Nonsingular complete curves

Nonsingular complete curves

Affine curves and complete curves

The projective plane and projective curves

Functions on the projective curve

Projective curves and valuations