Witt motives, transfers and reductive groups

1^st appeared online on the 16-7-2004 , updated on the 24-6-2006

In the first part of this preprint, we construct push-forwards (or transfers) along proper morphisms for the triangulated Witt groups of the bounded derived category of coherent sheaves on a regular Noetherian scheme of finite Krull dimension, and we prove the classical projection formula, base change formula and compatibility to composition. This first part has now been superseded by Tensor-triangulated categories and dualities and Push-forwards for Witt groups of schemes.

As applications, we construct a category of Witt motives and we obtain a theorem of dévissage (identification of the Witt groups with support in a closed regular subscheme with the Witt groups of this subscheme).