Thanks to nocredit for helping me - I initially asked nocredit for a profile picture and username for this post, but she told me she didn't need to be credited. I felt bad for not crediting her, so I decided to give her credit and no credit at the same time.

Table of Contents

• Introduction
• The Goal
• Atiyah-Macdonald
• Hartshorne
• Vakil
• Afterwards...

Introduction

Over the past two years, my interest in algebraic geometry has deepened considerably. In that time, I've made an effort to self-study through two foundational courses, Harvard Math 137 and Harvard Math 221, both of which helped shape my understanding of the field. However, while attending events like BIMSA's BMPSW and JMM 2025, I was repeatedly reminded of the gaps in my knowledge. This gap has also hindered my ability to dive into the representation theory I want to explore.

Since I was a sophomore in high school, people have recommended that I work through Hartshorne's Algebraic Geometry (especially chapters 2 and 3) and solve its exercises. Professor Matthew Emerton put it best:

I would suggest the following: a good grounding in algebraic geometry is essential. Most students in algebraic geometry, of all flavours, go through the rite of passage known as “Hartshorne”: reading Hartshorne's book, especially chapters 2 and 3, and solving vast numbers of exercises. It is more or less impossible, and in any case probably unwise, to avoid doing this. And once you have solved many/most of the Hartshorne problems, you should have some baseline confidence in algebraic geometry, scheme theory, and cohomology.

Despite hearing this advice for years, I never quite managed to take the plunge. In fact, I developed an irrational fear of Hartshorne's book. After roping in the most intelligent person I know into this project, I decided it's time to confront this head-on.

The Goal

Since algebraic geometry and commutative algebra are the same subject, I've decided to strengthen my understanding of commutative algebra as well.

The goal is simple to state: solve every problem in both Atiyah-Macdonald and Hartshorne.

Atiyah-Macdonald

Chapters read: 1 2 3

Hartshorne

Chapters read: 1

Vakil

Chapters read: 1

Afterwards...

Here's a long list of books to consider reading afterwards:

To be written later.