Deligne--Beilinson cohomology and log Hodge theory

TL;DR

This paper enhances the understanding of Deligne--Beilinson cohomology by integrating log Hodge theory, introducing a log relative version and proposing a fundamental conjecture in the field.

Contribution

It introduces a refined description of Deligne--Beilinson cohomology using log Hodge theory and presents a new conjecture in the area.

Findings

Improved description of Deligne--Beilinson cohomology with log Hodge theory

Introduction of the log relative version of the cohomology

Proposal of a fundamental conjecture in log Hodge theory

Abstract

We show that the description of Deligne--Beilinson cohomology is improved by using log Hodge theory. We consider the log relative version of it, and also present a fundamental conjecture in log Hodge theory.