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Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series

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arxiv 1802.09489 v3 pith:ROOYURY3 submitted 2018-02-26 math.NT math.AG

Jan Hendrik Bruinier , Tonghai Yang This is my paper · ORCID
classification math.NTmath.AG
keywords arithmeticspecialcoefficientsconjecturecyclesdefinitedegreeseisenstein
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Let V be a rational quadratic space of signature (m,2). A conjecture of Kudla relates the arithmetic degrees of top degree special cycles on an integral model of a Shimura variety associated with SO(V) to the coefficients of the central derivative of an incoherent Siegel Eisenstein series of genus m+1. We prove this conjecture for the coefficients of non-singular index T when T is not positive definite. We also prove it when T is positive definite and the corresponding special cycle has dimension 0. To obtain these results, we establish new local arithmetic Siegel-Weil formulas at the archimedean and non-archimedian places.

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  1. Kudla--Rapoport cycles and derivatives of local densities

    math.NT 2019-08 conditional novelty 8.0 of 10

    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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