Title: An Introduction to the K Theory of Varieties
Abstract: In this talk, I will introduce certain cut-and-paste invariants of algebraic varieties called motivic measures, or group homomorphisms from the Grothendieck ring of varieties, K_0(Var). With Zakharevich’s construction of the higher K groups of the category of varieties, there is an ongoing project to understand K_i(Var) by lifting these motivic measures (on the level of K_0) to derived motivic measures on the level of K_i for all i. I will describe some of this ongoing work, hopefully showing that there is interesting information recorded in K_i(Var), and it is understandable when i=1.