# Conservativity of realizations on motives of abelian type over finite fields

## TL;DR

This paper proves that the l-adic realization functor is conservative for Chow motives of abelian type over finite fields, with an extension to mixed motives, advancing understanding of motive realizations.

## Contribution

It establishes the conservativity of the l-adic realization functor on motives of abelian type over finite fields, including a weak extension to mixed motives.

## Key findings

- l-adic realization functor is conservative for Chow motives of abelian type
- Conservativity extends weakly to mixed motives of abelian type
- Advances understanding of motive realization over finite fields

## Abstract

We show that the l-adic realization functor is conservative when restricted to the Chow motives of abelian type over a finite field. A weak version of this conservativity result extends to mixed motives of abelian type.