Milnor-Witt motivic cohomology of complements of hyperplane arrangements

TL;DR

This paper computes the Milnor-Witt motivic cohomology of hyperplane arrangement complements, providing explicit algebraic descriptions and connecting to classical cohomology through realization.

Contribution

It offers the first explicit algebraic presentation of Milnor-Witt motivic cohomology for hyperplane arrangement complements and relates it to classical cohomology.

Findings

Explicit algebra with generators and relations for Milnor-Witt motivic cohomology

Connections established between motivic and classical cohomology

New computational tools for hyperplane arrangement complements

Abstract

In this paper, we compute the (total) Milnor-Witt motivic cohomology of the complement of a hyperplane arrangement in an affine space as an algebra with given generators and relations. We also obtain some corollaries by realization to classical cohomology.