Intersection theory, a topic at the heart of algebraic geometry, is concerned with the question of describing the intersection of two subvarieties in an ambient smooth algebraic variety. The modern flavour of the subject is highly influenced by Alexander Grothendieck’s revolutionary introduction of algebraic K-theory. In this course, we will introduce algebraic K-theory K0, as well as the closely related theory of Chow rings, of smooth algebraic varieties. We will mostly be occupied with understanding the basic properties of these theories and the precise relationship between the two.
Prerequisites: A good grasp of commutative algebra is necessary. The basics of scheme theory will also be assumed, at the level of Algebraic Geometry I, so at least attending that course concurrently is highly recommended.