# Mumford-Roitman argument on families

## TL;DR

This paper demonstrates that certain geometric properties, such as motivic decomposability and Chow decomposition, are preserved in special members of a family if they hold for a general member, highlighting a transfer principle in algebraic geometry.

## Contribution

It establishes a new transfer principle showing that properties like motivic decomposability are inherited by special members from general members within a family.

## Key findings

- Motivic decomposability transfers from general to special members.
- Chow theoretic decomposition of the diagonal also transfers within families.

## Abstract

The aim of this note is to show that the properties like motivic decomposability, Chow theoretic decomposition of the diagonal etc. happens for the special member of a family if it happens for a general member of the family.