Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

Andreas Mihatsch

Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

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arxiv 1611.06520 v2 pith:GSPJWUTC submitted 2016-11-20 math.AG

Andreas Mihatsch This is my paper · ORCID

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keywords arithmeticcomparisonfundamentalidentityisomorphismlemmarelativeahsendorf

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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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Kudla--Rapoport cycles and derivatives of local densities
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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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