Abstract

We generalize Fulton's intersection theory to the setting of motivic homotopy theory by developing the theory of fundamental classes, and establish (refined) Gysin maps and an excess intersection formula. The construction applies to some non-orientable cohomology theories such as hermitian K-theory and higher Chow-Witt groups. We also develop a theory of Euler classes of vector bundles and prove a motivic Gauss–Bonnet formula, which computes refined Euler characteristics in quadratic forms. This is a joint work with F. Déglise and A. Khan.