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.