Mixed objects are embedded into log pure objects

TL;DR

The paper demonstrates that mixed Hodge structures can be embedded into logarithmic pure Hodge structures, proposing a new approach to constructing the category of mixed motives using log pure motives.

Contribution

It introduces a novel embedding of mixed Hodge structures into logarithmic pure structures and suggests a simple construction for the category of mixed motives.

Findings

Mixed Hodge structures embed into log pure Hodge structures

A generalized embedding result is established

Implications for constructing mixed motives using log pure motives

Abstract

We prove that a variation of mixed Hodge structure is embedded in a logarithmic variation of pure Hodge structure, and a generalized version of this result. These results suggest some simple construction of the category of mixed motives by using log pure motives.