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PreprintarXiv licencearXiv

Contou-Carrère 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-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.

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Cite

BibTeXRIS
BibTeX
@misc{osipov2026contoucarrère,
  title = {{Contou-Carrère symbol, Deligne pairing and quintets}},
  author = {Denis V. Osipov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.14405},
  eprint = {2607.14405},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.14405},
}
RIS
TY  - UNPB
TI  - Contou-Carrère symbol, Deligne pairing and quintets
AU  - Denis V. Osipov
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2607.14405
UR  - https://arxiv.org/abs/2607.14405
AB  - 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.
ER  -