commutative algeba (summer 2024)

there are the "standard" references (that you can also find on the course website). below you find some personal favorites of mine and why i think they are good (all of them cover way more than is needed for the course):

• algebra chapter 0 by Aluffi, emphasizes a "categorical" viewpoint, introduces aspects of category theory at the "right" time, has a good exposition of some homological algebra

• grimoire d'algèbre commutative by Ramero, very exhaustive treatment of many topics of commutative algebra (in french), very useful if you want to study in the direction of adic spaces and Huber rings

• lectures notes on homological algebra and category theory from Bonn, where I learned homological algebra from (it does not contain any exotic material, but many details (also, it works with general abelian categories which is probably a good exercise in the beginning)). The old exercises from this course are also available here.

• course notes by Kato, for many beautiful thoughts on algebra and number theory, eg: "ℝ is like the sun, and the p-adics are like the stars. The sun blocks out the stars during the day, and humans are asleep at night and don’t see the stars, even though they are just as important"