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arXiv · 1802.09489

Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series

Jan Hendrik Bruinier·Tonghai Yang
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Abstract

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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Jan Hendrik Bruinier, Tonghai Yang. 2019-11-26. Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series. https://arxiv.org/abs/1802.09489

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