Green forms and the arithmetic Siegel-Weil formula

Abstract

We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conjecture put forward by Kudla relates these derivatives to arithmetic intersections of special cycles, and our results settle the part of his conjecture involving local archimedean heights.

References in corpus (3)

• On two arithmetic theta lifts
• Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series
• CM values of automorphic Green functions on orthogonal groups over totally real fields

Cited by in corpus (8)

• Kudla--Rapoport cycles and derivatives of local densities
• Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series
• Chow groups and $L$-derivatives of automorphic motives for unitary groups
• Arithmetic special cycles and Jacobi forms
• Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
• Double transgressions and Bott-Chern duality
• Pullback formulas for arithmetic cycles on orthogonal Shimura varieties
• Arithmetic Siegel-Weil formula on ${\mathcal{X}}_0(N)$