Arithmetic Gan–Gross–Prasad conjecture for RSZ unitary Shimura curves
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Published:2024-06-17
Issue:
Volume:
Page:1-19
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ISSN:1793-0421
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Container-title:International Journal of Number Theory
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language:en
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Short-container-title:Int. J. Number Theory
Affiliation:
1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, USA
Abstract
Xue proved an equational refinement of the unitary Shimura curve case of the arithmetic Gan–Gross–Prasad conjecture via the Gross–Zagier formula for quaternionic Shimura curves. On the other hand, Rapoport, Smithling and Zhang posed a variant of the conjecture, using modified PEL type Shimura varieties, which we call RSZ Shimura varieties. We reinterpret the result of Xue in terms of the modified Shimura curves. We then use the reinterpretation to prove a case of the variant of the conjecture. Our result combined with the work of Xue establishes a connection between the variant and the Gross–Zagier formula.
Funder
Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University
Publisher
World Scientific Pub Co Pte Ltd