Elden Elmanto

I will describe a coherence theorem for motivic fundamental classes. This latter object is a generalization of the fundamental classes in Chow groups, defined via deformation to the normal cone. This coherence is encoded in the homotopy theory of the so-called motivic infinite loop spaces, which are analogs in algebraic geometry of the topologist' notion of an infinite loop space. A consequence of the proof gives a universal property to the category of finite Chow-Witt correspondences of Calmès and Fasel. This is joint work with Hoyois, Khan, Sosnilo and Yakerson