论文标题
在振动的brauer群体上
On the Brauer groups of fibrations
论文作者
论文摘要
令$ \ Mathcal {x} \ rightarrow c $成为有限生成的字段$ k $之间的平滑不可值品种之间的主要形态，因此通用光纤$ x $是平稳，投射和几何连接的。假设$ c $是具有功能字段$ k $的曲线，我们在$ \ mathrm {pic}^0_ {x/k} $的Tate-Shafarevich组之间建立了一个关系，而几何brauer组则以$ \ Mathcal {x} $ {x} $和$ x $的utiverem和Grothered superrare和Grotherdieck cortialems prection of Artcal {x} $ \ Mathcal {x} $ heardirecl {x/k}建立关系。
Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible 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 for $\mathrm{Pic}^0_{X/K}$ and the geometric Brauer groups for $\mathcal{X}$ and $X$, generalizing a theorem of Artin and Grothendieck for fibered surfaces to arbitrary relative dimension.
