Let [Formula: see text] be a global field and let [Formula: see text] be a finite set of primes of [Formula: see text] containing the Archimedean primes. We generalize the duality theorem for the Néron [Formula: see text]-class group of an abelian variety [Formula: see text] over [Formula: see text] established previously by removing the requirement that the Tate–Shafarevich group of [Formula: see text] be finite. We also derive an exact sequence that relates the indicated group associated to the Jacobian variety of a proper, smooth and geometrically connected curve [Formula: see text] over [Formula: see text] to a certain finite subquotient of the Brauer group of [Formula: see text].

中文翻译：

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Brauer 群和 Néron 类群

令 [Formula: see text] 是一个全局域，让 [Formula: see text] 是 [Formula: see text] 的有限素数集，其中包含阿基米德素数。我们通过删除 [Formula: 的 Tate-Shafarevich 群的要求：见正文] 是有限的。我们还推导出一个精确序列，该序列将与 [公式：参见文本] 上 [公式：参见文本] 的适当、平滑和几何连接曲线 [公式：参见文本] 的雅可比变体相关的指示组与 [公式的布劳尔群的某个有限子商相关联: 见正文]。