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.
Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma
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abstract
We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension. The main ingredient for this reduction is a comparison isomorphism between different moduli problems of PEL-type for p-divisible groups. The construction of this comparison isomorphism is based on the theory of relative displays and frames, as developed by Tobias Ahsendorf, Eike Lau and Thomas Zink.
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2019 1verdicts
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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.