For an arithmetic surface , the Deligne pairing gives the “schematic contribution” to the Arakelov intersection number. We present an idelic and adelic interpretation of the Deligne pairing; this is the first crucial step for a full idelic and adelic interpretation of the Arakelov intersection number. For the idelic approach, we show that the Deligne pairing can be lifted to a pairing , where is an important subspace of the two-dimensional idelic group . On the other hand, the argument for the adelic interpretation is entirely cohomological.
Kyoto J. Math.
62(2):
433-470
(June 2022).
DOI: 10.1215/21562261-2022-0009
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