Yet another version of Mumford's theorem

TL;DR

This paper presents a variant of Mumford's theorem, showing that for a general variety, all Chow groups are maximally large and cannot be confined to divisors, highlighting their extensive structure.

Contribution

It introduces a new variant of Mumford's theorem demonstrating the maximal size of Chow groups for general varieties.

Findings

Chow groups are as large as possible for general varieties.

Chow groups cannot be supported on divisors.

The result extends Mumford's original theorem.

Abstract

The aim of this note is to provide a variant statement of Mumford's theorem. This variant states that for a general variety, all Chow groups are "as large as possible", in the sense that they cannot be supported on a divisor.