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 $(\mathrm{L}{f}^{\ast },\mathrm{R}{f}_{\ast })$ and $(\mathrm{R}{f}_{\ast },f^{!})$ (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.