Abstract
For an arithmetic surface X→B=SpecOK, the Deligne pairing ⟨,⟩:Pic(X)×Pic(X)→Pic(B) 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 ⟨,⟩i:ker(d×1)×ker(d×1)→Pic(B), where ker(d×1) is an important subspace of the two-dimensional idelic group AX×. On the other hand, the argument for the adelic interpretation is entirely cohomological.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
