Speaker:  Stephen McKean (Harvard University) 

Title: Motivic Euler characteristics and power structures

Abstract: There is a quadratic form-valued version of the compactly supported Euler characteristic coming from motivic homotopy. A feature of this Euler characteristic is that it descends to a ring homomorphism out of the Grothendieck ring of varieties. In characteristic 0, this Euler characteristic was constructed by Röndigs and later Arcila-Maya—Bethea—Opie—Wickelgren—Zakharevich, who used Bittner’s blow up presentation of K_0(Var). In characteristic not 2, Azouri gave a characterization in terms of the six functor formalism. I will discuss a hybrid approach using a sort of universal property of K_0(Var). I will then discuss power structures on K_0(Var) and the Grothendieck—Witt ring of quadratic forms, and conclude with a conjecture relating these two power structures. This is joint work in progress with Dori Bejleri