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Apart from the Deligne's original paper "Le déterminant de la cohomologie", is there any other reference presenting the construction of the Deligne pairing on arithmetic surfaces?

Of course there is "nothing wrong" with the original paper, I'm only looking for other sources.

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    $\begingroup$ The Deligne bracket is also discussed in pub.math.leidenuniv.nl/~jongrsde/publications/thesis.pdf . You can also have a look at the work of Dennis Eriksson $\endgroup$
    – Ariyan Javanpeykar
    Commented Sep 10, 2016 at 15:40
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    $\begingroup$ The theory has been extended to higher dimensions by Renée Elkik. See her two papers, Annales scientifiques de l'École normale supérieure (construction of the intersection line bundle) and Duke Math. Journal (definition of a metric in the Arakelov case). $\endgroup$
    – ACL
    Commented Sep 28, 2016 at 22:09

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See Arbarello/Cornalba/Griffiths: "Geometry of algebraic curves II" p. 366-379.

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