On the Brauer groups of fibrations

Zusammenfassung

Let X →C be a flat k-morphism between smooth integral varieties over a finitely generated
field k such that the generic fiber X is smooth, projective and geometrically connected.
Assuming that C is a curve with function field K, we build a relation between the Tate-
Shafarevich group of Pic0
X/K and the geometric Brauer groups of X and X, generalizing a
theorem of Artin and Grothendieck for fibered surfaces to higher relative dimensions.