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Algebra and Geometry Seminar

Monday, November 15, 2021
4:00pm to 5:00pm
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Linde Hall 387
A compactly supported motivic Euler characteristic via the Hochschild complex
Morgan Opie, Department of Mathematics, UCLA,

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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].