The motivic Thom isomorphism
arXiv:math/0306151
Abstract
The existence of a good theory of Thom isomorphisms in some rational category of mixed Tate motives would permit a nice interpolation between ideas of Kontsevich on deformation quantization, and ideas of Connes and Kreimer on a Galois theory of renormalization, mediated by Deligne's ideas on motivic Galois groups.
Talk at the Newton Institute, December 2002; final version, to appear in the Conference Proceedings