Correspondences in log Hodge cohomology

TL;DR

This paper develops a framework for constructing correspondences in logarithmic Hodge theory over perfect fields, generalizing previous work and relaxing key conditions to broaden applicability.

Contribution

It introduces new methods to construct logarithmic Hodge correspondences, extending prior theories to more general settings and less restrictive conditions.

Findings

Constructed correspondences in log Hodge cohomology with log poles and zeroes.

Generalized non-logarithmic Hodge correspondences to the logarithmic setting.

Relaxed finiteness and strictness conditions on correspondences.

Abstract

We construct correspondences in logarithmic Hodge theory over a perfect field of arbitrary characteristic. These are represented by classes in the cohomology of sheaves of differential forms with log poles and, notably, log zeroes on cartesian products of varieties. From one perspective this generalizes work of Chatzistamatiou and R\"ulling, who developed (non-logarithmic) Hodge correspondences over perfect fields of arbitrary characteristic; from another we provide partial generalizations of more recent work of Binda, Park and {\O}stv{\ae}r on logarithmic Hodge correspondences by relaxing finiteness and strictness conditions on the correspondences considered.