发表机构
Steklov International Mathematical Center（斯捷克洛夫国际数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究仿射基概型上射影曲线的互反律，其推广了韦伊互反律等。应用互反律描述群ind-概型中心扩张对五元组模栈上线丛的作用，该模栈上线丛由五元组中线丛的德利涅配对构造。
AI 中文摘要
我们证明了仿射基概型上一族射影曲线的互反律，其中曲线可以是奇异且可约的，基可以是非诺特的。这些互反律推广了域上射影曲线的韦伊互反律和Contou-Carrère符号的互反律。我们应用已证明的互反律来描述与形式穿孔圆盘相关的群 ind-概型的某些中心扩张对五元组模栈上某些线丛的作用。五元组由一族曲线上的几何数据组成，包括该族上的一个线丛。模栈上的线丛是利用五元组中线丛的德利涅配对构造的。
英文摘要
We prove the reciprocity laws for a family of projective curves over an affine base scheme, where curves can be singular and reducible, and the base can be non-Noetherian. These reciprocity laws generalize the Weil reciprocity law for a projective curve over a field and the reciprocity law for the Contou-Carrère symbol. We apply the proven reciprocity laws to describe the actions of certain central extensions of the group ind-scheme related with the formal punctured disc on certain line bundles on the moduli stacks of quintets. A quintet consists of geometric data including a family of curves and a line bundle on this family. The line bundles on the moduli stacks are constructed using the Deligne pairings of line bundles from quintets.
Comments30 pages; minor changes
