Algebra and Geometry Seminar

The motivic Euler characteristic of a smooth, projective variety over a field k is an invariant that takes values in the Grothendieck--Witt group GW(k) of equivalence classes of bilinear forms over k. In this talk, we will show that the motivic Euler characteristic over a field k of characteristic zero can be defined using the Hochschild complex together with a canonical bilinear form. Our definition induces a map from the Grothendieck group of k-varieties to GW(k), extending the definition of the motivic Euler characteristic to all varieties over k. As time permits, we will discuss the possibility of lifting this map to a spectrum-level construction. This is joint work with Niny Arcila-Maya, Candace Bethea, Kirsten Wickelgren, and Inna Zakharevich.