Height pairings on Shimura curves and p-adic uniformization
Abstract
We establish a relation between intersection numbers of special cycles on a Shimura curve and special values of derivatives of metaplectic Eisenstein series at a place of bad reduction where p-adic uniformization in the sense of Cherednik and Drinfeld holds. The result extends the one established by one of us (S. Kudla: Ann. of Math. 146 (1997)) for the archimedean place and for the non-archimedean places of good reduction. The bulk of the paper is concerned with the corresponding problem on the Drinfeld upper half plane (the formal scheme version).
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- September 1998
- DOI:
- 10.48550/arXiv.math/9809149
- arXiv:
- arXiv:math/9809149
- Bibcode:
- 1998math......9149K
- Keywords:
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- Algebraic Geometry;
- 11F27 (Primary) 11G10;
- 14G35 (Secondary)
- E-Print:
- 82 pages, 1 figure, Postscript