## Weekly outline

**Schedule**See Orlando's webpage: orlandomarigliano.com/course22

**Exercises**- Exercises (
**do**contribute to final grade; hand in Exercise*n*by 11:59pm on the Wednesday before the (*n+1*)th lecture on the Thursday via Kurser, using the links at the bottom of this page, making sure to click "Submit" after uploading the PDF) -
Challenging exercises (do
**not**contribute to final grade)

**Lecture Notes**- Here are some lecture notes for the first part of the course.
- The lecture notes for TA session (Krull dimension) 2022-11-03.

**Book**The first part of the course will follow the book "Introduction to Commutative Algebra" by Atiyah and Macdonald (which you can find online). The pacing will be roughly half of a chapter per lecture, so that lectures 1–8 will cover chapters 1–4.

**Update:**Lecture 7 will cover chapter 4, Lecture 8 will cover Noetherian rings and primary decomposition in Noetherian rings (a selection of topics in Chapters 6 and 7).**Update 2:**Lecture 8 will also cover Hilbert's Nullstellensatz, the 'strong form' found in Ch. 7, Exercise 14 of the book.The second part of the course will follow the book "An Invitation to Algebraic Geometry" by Smith, Kahanpää, Kekäläinen, and Traves (which you can also find online). We will try to finish the first 4 chapters, but we will already have covered much more than the necessary algebraic prerequisites, so some parts (e.g. a lot of chapter 2) will go rather quick. In general, we will skip over the lengthier proofs and some of the more technical aspects with the hope of being able to talk about the more applied/geometric/physical topics towards the end of the course. (Another nice reference for this half of the course is Shafarevich's "Basic Algebraic Geometry 1").

Supplementary material – not covered in Atiyah-Macdonald, might be useful for the exercises or for understanding in general.**Supplementary Material**

**Examination and grading**The final (and only) exam for this course will take place on the

**5th of January, 2023**(with the re-examination taking place on the**13th of February, 2023**). The exam will give you a percentile score. Regularly handing in solutions to the weekly exercises will improve this score, adding an amount of percentage points on top of it. Your final grade will be determined by this combined score. In other words,**not**completing the exercises will**not lower**your final score, but (successfully)**completing**the exercises**will increase**your final score. The specifics of this system are not yet fixed, but will be communicated at some point around the middle of the term.**Teachers**Lecturers: Orlando Marigliano (orlandom@kth.se) and Tim Hosgood (tim.hosgood@math.su.se)

Assistants: Vahid Shahverdi (vahidsha@kth.se) and Sjoerd Wijnand de Vries (sjoerd.devries@math.su.se)

**Office hours****Tim's**office hours:**Tuesdays**and**Thursdays**,**14:00–15:00**in**Albano Hus 1, floor 3**or**on Zoom**.I will

**not**help with the weekly exercises (i.e. those that can contribute to your final grade) until**after**the date on which they are due to be handed in, but we can happily discuss past weeks' exercises, the bonus "challenging exercises", or anything else! I don't have anything planned for these sessions — this is just 2 hours a week that I intend to keep free for any questions you might have.If you need access to the department (because you don't have a keycard), or if you wish to meet on Zoom, then please just send me an email in advance and I will either arrange to let you in or send you a Zoom link.

**Official course pages**- Exercises (