Weights and conservativity

TL;DR

This paper investigates conservativity in triangulated categories with weight structures and demonstrates weight conservativity for l-adic realizations of motives of Abelian type in characteristic zero.

Contribution

It introduces the concept of conservativity within triangulated categories with weight structures and proves a key conservativity result for l-adic realizations of motives of Abelian type.

Findings

Establishes weight conservativity for l-adic realizations

Provides a framework for studying conservativity in triangulated categories

Applies results to motives of Abelian type in characteristic zero

Abstract

The purpose of this article is to study conservativity in the context of triangulated categories equipped with a weight structure. As application, we establish (weight) conservativity for the restriction of the (generic) l-adic realization to the category of motives of Abelian type of characteristic zero.