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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 Sep 10 '16 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 Sep 28 '16 at 22:09
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See Arbarello/Cornalba/Griffiths: "Geometry of algebraic curves II" p. 366-379.

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