论文标题
Brauer群和od oltale同型类型
Brauer groups and étale homotopy type
论文作者
论文摘要
在复杂的分析空间的背景下，将Schröer的结果扩展在一个格伦迪克问题上，我们证明了Brauer Map $δ的过滤性$δ：Br（x）\ rightarrow H _ {\rmét}^2（x，x，x，x，\ mathbb {g}他们的典型同型类型。我们使用代数$ K（π，1）$空间的属性将其应用于某些类别的适当和平滑的代数方案。特别是，我们恢复了Hoobler和Berkovich作为Abelian品种的结果。此外，我们为$δ$的溢流性提供了额外的条件，涉及$δ$。所有提出的条件都与平滑准标记品种相当。
Extending a result of Schröer on a Grothendieck question in the context of complex analytic spaces, we prove that the surjectivity of the Brauer map $δ: Br(X) \rightarrow H_{\rm ét}^2(X,\mathbb{G}_{m, X})_{\rm tor}$ for algebraic schemes depends on their étale homotopy type. We use properties of algebraic $K(π, 1)$ spaces to apply this to some classes of proper and smooth algebraic schemes. In particular we recover a result of Hoobler and Berkovich for abelian varieties. Further, we give an additional condition for the surjectivity of $δ$ which involves pro-universal covers. All proposed conditions turn out to be equivalent for smooth quasi-projective varieties.
