Filtering the Grothendieck ring of varieties

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]+[XY] 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.

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Affiliation

University of Chicago; Member, School of Mathematics