Degeneration Data for Additional Structures
Degeneration Data for Additional Structures
This chapter supplies a theory of degeneration data for endomorphism structures, Lie algebra conditions, and level structures, based on the theory of degeneration in Chapter 4. People often claim that the degeneration theory for general PEL-type structures is just a straightforward consequence of the functoriality of the merely polarized case. However, the Weil-pairing calculation carried out in this chapter may suggest that this is not true. As this chapter shows, functoriality does not seem to imply properties about pairings in an explicit way. There are conceptual details to be understood beyond simple implications of functoriality. However, this chapter is able to present a theory of degeneration data for abelian varieties with PEL structures, together with the notion of cusp labels.
Keywords: degeneration theory, degeneration data, endomorphism structures, Lie algebra conditions, level structures, PEL-type structures, functoriality, Weil-pairing calculation, cusp labels
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
