Finite Chow-Witt correspondences

1^st appeared online on the 8-12-2014

We first introduce finite Chow-Witt correspondences and then use them to define generalized motivic cohomology groups, also called Milnor-Witt motivic cohomology groups mapping to the classical motivic cohomology groups of Voevodsky. Our construction is based on a new definition of (usual) finite correspondences in which Chow groups appear explicitely. We then more or less formally replace them by Chow-Witt groups with coefficients in appropriate line bundles.