Let CM Φ be the (integral model of the) stack of principally polarized CM Abelian varieties with a CM-type Φ. Considering a pair of nearby CM-types (i.e. such that they are different in exactly one embedding) Φ 1 , Φ 2 , we let X = CM Φ 1 × CM Φ 2 and define arithmetic divisors Z(α) on X such that the Arakelov degree of Z(α) is (up to multiplication by an explicit constant) equal to the central value of the α th coefficient of the Fourier expansion of the derivative of a Hilbert Eisenstein series.
In this paper, we prove the relation between special cycles on a Rapoport-Smithling-Zhang Shimura variety and special values of the derivative of a Hilbert Eisenstein series.
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