Cycle theory of relative correspondences

TL;DR

This paper develops a comprehensive theory of complexes of relative correspondences, extending existing theories for smooth projective varieties, with applications to constructing the triangulated category of motives over a base variety.

Contribution

It introduces a generalized framework for complexes of relative correspondences, broadening the scope of the classical theory for smooth projective varieties.

Findings

Establishment of a new theory of complexes of relative correspondences

Extension of classical correspondence theory to relative settings

Foundation for constructing triangulated categories of motives

Abstract

We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of the triangulated category of motives over a base variety.