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.