# Filtering the Grothendieck ring of varieties

 Members' Seminar Topic: Filtering the Grothendieck ring of varieties Speaker: Inna Zakharevich Affiliation: University of Chicago; Member, School of Mathematics Date: Monday, March 10 Time/Room: 2:00pm - 3:00pm/S-101 Video Link: https://video.ias.edu/members/2014/0310-InnaZakharevich

The Grothendieck ring of varieties over $k$ is defined to be the free abelian group generated by varieties over $k$, modulo the relation $[X] = [Y] + [X \backslash Y]$ for all $X$ and closed subvarieties $Y$. Multiplication is induced by cartesian product. Using algebraic K-theory and purely geometric intuition we present a categorification of this ring. This category carries a filtration which does not exist on the ring. This allows us to construct a spectral sequence whose 0th column converges to the Grothendieck ring of varieties and identify the next column.