# Chow motives without projectivity, II

## TL;DR

This paper presents a simplified method for constructing intermediate extensions of Chow motives under specific weight conditions, compares it to existing theories, and reviews applications to Shimura varieties.

## Contribution

It introduces a new simplified construction of intermediate Chow motives, expanding the theoretical framework and connecting it with previous interior motive theory.

## Key findings

- Provides a criterion for the absence of weights in the boundary
- Establishes a simplified construction method for Chow motives
- Reviews applications to Shimura varieties boundary

## Abstract

The purpose of this article is to provide a simplified construction of the intermediate extension of a Chow motive, provided a condition on absence of weights in the boundary is satisfied. We give a criterion, which guarantees the validity of the condition, and compare our new construction to the theory of the interior motive established earlier. We finish the article with a review of the known applications to the boundary of Shimura varieties.