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On Shimura varieties for unitary groups
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This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian varieties with additional structure, and which admit interesting algebraic cycles. We generalize to arbitrary signature type the results of our previous work valid under special signature conditions. We compare our Shimura varieties with other unitary Shimura varieties.
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Cited by 2 Pith papers
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Weil representation and Arithmetic Fundamental Lemma
A global proof of the arithmetic fundamental lemma for unitary groups over Q_p (odd p >= n) via an SL_2-equivariant relative trace formula and derived CM cycles, which also yields the Jacquet-Rallis fundamental lemma ...
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Kudla--Rapoport cycles and derivatives of local densities
The authors prove the local and global Kudla-Rapoport conjectures and, combining with results of Liu and Garcia-Sankaran, the arithmetic Siegel-Weil formula in arbitrary dimension.
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