论文标题
在数字场上，还原群体的GALOIS共同体中定位的溢流性标准
Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field
论文作者
论文摘要
让$ g $是一个在数字字段$ f $上的连接还原组，让$ s $是$ f $的位置（有限或无限）。我们给出了必要且充分的条件，以从$ h^1（f，g）$溢出到集合$ h^1（f_v，g）$的“直接总和”，其中$ v $在$ s $上运行。在附录中，我们为一个任意特征领域的还原群体的Abelian Galois共同学提供了新的结构。
Let $G$ be a connected reductive group over a number field $F$, and let $S$ be a set (finite or infinite) of places of $F$. We give a necessary and sufficient condition for the surjectivity of the localization map from $H^1(F,G)$ to the "direct sum" of the sets $H^1(F_v,G)$ where $v$ runs over $S$. In the appendices, we give a new construction of the abelian Galois cohomology of a reductive group over a field of arbitrary characteristic.
