Abstract We give a reformulation of the Birch and Swinnerton-Dyer conjecture over global function fields in terms of Weil-etale cohomology of the curve with coefficients in the Neron model, and show that it holds under the assumption of finiteness of the Tate-Shafarevich group.

中文翻译：

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函数域上的 Birch 和 Swinnerton-Dyer 公式的 Weil-étale 版本

摘要 我们根据 Neron 模型中系数曲线的 Weil-etale 上同调重新表述了全局函数域上的 Birch 和 Swinnerton-Dyer 猜想，并表明它在 Tate-Shafarevich 群有限性假设下成立.