TITLE: What is Mumford's example of a normal complex algebraic surface $X$ with non-torsion elements in $H^2_{et}(X,\mathbb{G}_m)$?
QUESTION [6 upvotes]: I have heard that Mumford has constructed an example of a normal complex algebraic surface $X$ such that $H^2_{et}(X,\mathbb{G}_m)$ contains a non-torsion element. But I cannot find the reference.
Then what is the surface $X$ and how to construct a non-torsion element in $H^2_{et}(X,\mathbb{G}_m)$?

REPLY [4 votes]: In [Milne, Étale Cohomology], p. 146, Remark IV.2.8, there is a reference to [Grothendieck, Le groupe de Brauer. In: Dix Exposés sur la Cohomologie des Schémas], II.1.11b. (see https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/DixExp.pdf)