Abstract
We study the intersections of special cycles on a unitary Shimura variety of signature $(n-1,1)$ and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures of Kudla and suggest a Gross-Zagier theorem for unitary Shimura varieties.
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@book {AMRT, MRKEY = {2590897},
AUTHOR = {Ash, Avner and Mumford, David and Rapoport, Michael and Tai, Yung-sheng},
TITLE = {Smooth Compactifications of Locally Symmetric Varieties},
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AUTHOR = {Kudla, Stephen S.},
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AUTHOR = {Kudla, Stephen S. and Rapoport, Michael},
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AUTHOR = {Messing, William},
TITLE = {Travaux de {Z}ink},
BOOKTITLE = {S{é}minaire Bourbaki. Vol. 2005/2006},
SERIES = {Astérisque},
FJOURNAL = {Astérisque},
VOLUME = {311},
YEAR = {2007},
PAGES = {Exp. No. 964, ix, 341--364},
ISSN = {0303-1179},
ISBN = {978-2-85629-230-3},
MRCLASS = {14L05 (14B12 14F30)},
MRNUMBER = {2359049},
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JOURNAL = {Astérisque},
FJOURNAL = {Astérisque},
NUMBER = {312},
YEAR = {2007},
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NUMBER = {2, part 1},
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AUTHOR = {Zink, Thomas},
TITLE = {The display of a formal {$p$}-divisible group},
BOOKTITLE = {Cohomologies $p$-Adiques et Applications Arithm{é}tiques, I},
SERIES = {Astérisque},
FJOURNAL = {Astérisque},
VOLUME = {278},
YEAR = {2002},
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ISSN = {0303-1179},
MRCLASS = {14L05 (14F30)},
MRNUMBER = {1922825},
MRREVIEWER = {Oliver B{ü}ltel},
ZBLNUMBER = {1008.14008},
}