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 Mat. Sb., 2006, Volume 197, Number 1, Pages 25–38 (Mi msb1494)

Poincaré biextension and idèles on an algebraic curve

S. O. Gorchinskiy

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The Weil pairing of two elements of the torsion of the Jacobian of an algebraic curve can be expressed in terms of the product of the local Hilbert symbols of two special idèles associated with the torsion elements of the Jacobian. On the other hand, Arbarello, De Concini, and Kac have constructed a central extension of the group of idèles on an algebraic curve in which the commutator is also equal up to a sign to the product of all the local Hilbert symbols of two idèles.
The aim of the paper is to explain this similarity. It turns out that there exists a close connection between the Poincaré biextension over the square of the Jacobian defining the Weil pairing and the central extension constructed by Arbarello, de Concini, and Kac. The latter is a quotient of a certain biextension associated with the central extension.
Bibliography: 6 titles.

DOI: https://doi.org/10.4213/sm1494

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English version:
Sbornik: Mathematics, 2006, 197:1, 23–36

Bibliographic databases:

UDC: 512.7
MSC: 14H40, 14H25, 19F15

Citation: S. O. Gorchinskiy, “Poincaré biextension and idèles on an algebraic curve”, Mat. Sb., 197:1 (2006), 25–38; Sb. Math., 197:1 (2006), 23–36

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb1494
• https://doi.org/10.4213/sm1494
• http://mi.mathnet.ru/eng/msb/v197/i1/p25

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. O. Gorchinskiy, “An adelic resolution for homology sheaves”, Izv. Math., 72:6 (2008), 1187–1252
2. Gorchinskiy S., “Notes on the Biextension of Chow Groups”, Motives and Algebraic Cycles: a Celebration in Honour of Spencer J. Bloch, Fields Institute Communications, 56, 2009, 111–148
3. L. A. Takhtajan, “Quantum field theories on algebraic curves. I. Additive bosons”, Izv. Math., 77:2 (2013), 378–406
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