Brauer groups and cohomology

We explain in an elementary way an example showing that the Brauer group of a scheme X does not always coincide with the torsion of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H^{2} (X,\mathbb{G}_{m} ). $$ \end{document}