Push-forwards for Witt groups of schemes

TL;DR

This paper introduces a new method for defining push-forward maps in Witt groups of schemes using Grothendieck duality, linking advanced categorical theories with classical derived functors.

Contribution

It develops a framework for push-forwards in Witt groups of schemes based on Grothendieck duality, extending previous categorical results to algebraic geometry.

Findings

Defined push-forwards for Witt groups along proper morphisms

Connected tensor-triangulated categories with classical derived functors

Applied duality theory to scheme-based Witt groups

Abstract

We define push-forwards for Witt groups of schemes along proper morphisms, using Grothendieck duality theory. This article is an application of results of the authors on tensor-triangulated closed categories to such structures on some derived categories of schemes together with classical derived functors.