Lecture 1 (8/30/2022): Introduction and overview of Cycles and K-theory
Lecture 2 (9/1/2022): Cycles, rational equivalence, pushing forward and pulling back
Lecture 3 (9/6/2022): Towards intersections: the first Chern class of a line bundle
Lecture 4 (9/8/2022): A taste of Chow group of vector bundles (towards the Gysin pullback maps and intersections)
Lecture 5 (9/13/2022): (getting stuck with a) Normal cones example
Lecture 6 (9/15/2022): Deformation to the normal cone and intersection products summary, from Chern classes to K-theory
Lecture 7 (9/20/2022): About Riemann-Roch
Lecture 8 (9/27/2022): Oriented cohomology theories
Lecture 9 (9/29/2022): Statement of the Panin-Smirnov-Grothendieck-Hirzebruch-Riemann-Roch Theorem
Lecture 10 (10/4/2022): Classical (lower) K-theory
Lecture 11 (10/11/2022): Towards higher K-theory: Q construction and nerves
Lecture 12 (10/13/2022): Localization, devissage, and resolution.
Lecture 13 (10/18/2022): Q-construction facts and pushforwards.
Lecture 14 (10/20/2022): Projective bundles, introduction to division algebras and Galois cohomology.
Lecture 15 (10/25/2022): The story of algebraic structures, introduction to the Brown-Gersten-Quillen spectral sequence.
Lecture 16 (10/27/2022): Localization and support, towards the BGQ sequence.
Lecture 17 (11/1/2022): The BGQ sequence, definition of the Severi-Brauer varieties.
Lecture 18 (11/3/2022): The BGQ sequence, definition of the Severi-Brauer varieties.
Lecture 19 (11/8/2022): The end of the Merkurjev-Suslin Theorem (assuming the beginning).
Lecture 20 (11/10/2022): Hilbert 90 for K2, assuming some facts.
Lecture 21 (11/17/2022): Reducing to the case of surjectivity of the norm, assuming facts about the K-cohomology of Severi-Brauer varieties.
Lecture 22 (11/29/2022): Recap on reduction to information about K-cohomology of Severi-Brauer varieties.
Lecture 23 (12/1/2022): The Brauer group and representations of Lie algebras. From H1(K2) to Chow, part 1.
