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arXiv · 2607.14405

Contou-Carr\`ere symbol, Deligne pairing and quintets

Denis V. Osipov
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Abstract

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-Carr\`ere 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.

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Denis V. Osipov. 2026-07-15. Contou-Carr\`ere symbol, Deligne pairing and quintets. https://arxiv.org/abs/2607.14405

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