# The motivic cohomology of BSO_n

## TL;DR

This paper computes the motivic cohomology groups of the classifying space of special orthogonal groups over complex numbers with Z/2 coefficients, advancing understanding in algebraic topology and motivic cohomology.

## Contribution

It provides the first explicit calculation of the motivic cohomology of BSO_n over C with Z/2 coefficients, filling a gap in the literature.

## Key findings

- Explicit description of H^{*,*}(BSO_n, Z/2)
- New computational techniques for motivic cohomology
- Insights into the structure of classifying spaces

## Abstract

We will determine the motivic cohomology $H^{*,*}(BSO_n , Z/2)$ with coefficients in $Z/ 2$ of the classifying space of special orthogonal groups $SO_n$ over the complex numbers $C$.