Push-forwards for Witt groups of schemes

Abstract

Using suitable closed symmetric monoidal structures on derived categories of schemes, as well as adjunctions of the type ({\rm L}f^*,{\rm R}f_*) and ({\rm R}f_*,f^!) (i.e. Grothendieck duality theory), we define push-forwards for coherent Witt groups along proper morphisms between separated noetherian schemes. We also establish fundamental theorems for these push-forwards (e.g. base change and projection formula) and provide some computations.