Algebraic K-theory and intersection theory

 
 

Time and place

Winter semester 2019/20
Wednesdays 10-12, M 009

Exercise sessions

Fridays 10-12 in M009
by Maria Yakerson

Description

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.

 

References

[G] Alexander Grothendieck, Classes de faisceaux et théorème de Riemann–Roch, pdf

[L] Marc Levine, A short course in K-theory, pdf

Typed lecture notes will also be provided.

Contact

adenullel.khanull[email protected]nullhematik.uni-renullgensburg.dnulle