Descent of algebraic cycles

TL;DR

This paper characterizes certain morphisms that satisfy descent of algebraic cycles integrally, introduces a naive pull-back of cycles for arbitrary morphisms, and proves its basic properties.

Contribution

It provides a characterization of universally generalizing morphisms satisfying cycle descent and introduces a new naive pull-back for arbitrary morphisms.

Findings

Characterization of universally generalizing morphisms with cycle descent.

Introduction of a naive pull-back of cycles for arbitrary morphisms.

Proof of basic properties of the naive pull-back.

Abstract

We characterize universally generalizing morphisms which satisfy descent of algebraic cycles integrally as those universally generalizing morphisms which are surjective with generically reduced fibres. In doing so, we introduce a naive pull-back of cycles for arbitrary morphisms between noetherian schemes, which generalizes the classical pull-back for flat morphisms, and then prove basic properties of this naive pull-back.