This term I am teaching Introduction to schemes: all the materials will be here.

I plan to be using lecture notes by Dhruv Ranganathan, enjoy!

In spring 2023, I taught a Master's course (M2) at Sorbonne.

- Chapter 0 - Introduction
- Chapter 1 - K_0 of rings
- Chapter 2 - K_1 of rings
- Chapter 3 - K-theory space
- Chapter 4 - K_0 vs Chow groups
- Chapter 5 - K-theory of schemes
- Chapter 6 - Rigidity theorem
- Chapter 7 - Motivic cohomology
- Extra lecture by Elden Elmanto

**Helpful sources:**

- M. Hoyois’ lecture course on algebraic K-theory
- A. Khan’s lecture course on algebraic K-theory and intersection theory
- F. Binda and A. Khan’s lecture course on Grothendieck-Riemann-Roch theorem
- D. Nardin's lecture course on Stable homotopy theory
- S. Kelly "User's guide to Voevodsky's correspondences"
- D. Grayson "Motivic spectral sequence"
- T. Bachmann "Algebraic K-theory from the viewpoint of motivic homotopy theory"

**Useful references:**

- C. Weibel "The K-book: an introduction to algebraic K-theory", 2013
- E. Friedlander, D. Grayson "Handbook of K-theory", 2005
- C. Mazza, C. Weibel, V. Voevodsky "Lecture notes on motivic cohomology", 2006
- D. Quillen "Higher algebraic K-theory: I", 1973
- R. Thomason and T. Trobaugh “Higher algebraic K-theory of schemes and of derived categories”, 1990
- A. Suslin "On the K-theory of algebraically closed fields", 1983
- C. Weibel “Algebraic K-theory of rings of integers in local and global fields”, 2004

"A wise man loves to learn, and a fool loves to teach."

Anton Chekhov, From the diaries

In SS 2022 I taught "Introduction to Algebraic Geometry" at ETH.

My main source were the notes by G. Ellingsrud and J.C. Ottem

which contain pictures, intuition and comments in Norwegian!

- Chapter 0 - Introduction
- Chapter 1 - Algebraic sets
- Chapter 2 - Zariski topology
- Chapter 3 - Sheaves and varieties
- Chapter 4 - Projective varieties
- Chapter 5 - Dimension revisited
- Chapter 6 - Smoothness and singularities
- Chapter 7 - Birationality
- Chapter 8 - Curves
- Chapter 9 - Properties of morphisms
- Chapter 10 - Bezout theorem (notes by J. Ottem)
- Chapter 11 - Prime spectrum
- Chapter 12 - Schemes
- Chapter 13 - Weil conjectures

Send me your favourite ones!

- W. Thurston "On proof and progress in mathematics"
- W. Thurston "What's a mathematician to do?"
- J. Littlewood "The mathematician's art of work"
- W. Gowers "The two cultures of mathematics"
- P. Lockhart "A mathematician's lament"
- T. Tao "Does one have to be a genius to do math?"
- T. Tao "On time management"
- T. Tao "Enjoy your work"
- "Steps to solving a math problem"

E-mail: yakerson at imj-prg.fr