# Cohomology and the Brauer groups of diagonal surfaces

## TL;DR

This paper introduces a method for computing the Brauer group of diagonal surfaces, specifically diagonal quartic surfaces over Q and Q(i), advancing understanding of their algebraic structure.

## Contribution

The paper provides a new approach for calculating Brauer groups of diagonal surfaces, including explicit results for quartic surfaces over Q and Q(i).

## Key findings

- Calculated Brauer groups for diagonal quartic surfaces over Q.
- Determined Brauer groups over Q and Q(i) for these surfaces.
- Developed a general method for such calculations.

## Abstract

We present a method for calculating the Brauer group of a surface given by a diagonal equation in the projective space. For diagonal quartic surfaces with coefficients in Q we determine the Brauer groups over Q and Q(i).