Special cycles on unitary Shimura varieties II: global theory

By S. Kudla, Michael Rapoport. 2009

95 citations recorded by the source corpus.

We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n-1, 1). We define arithmetic cycles on these models and study their intersection behaviour. In particular, in the non-degenerate case, we prove a relation between their intersection numbers and Fourier coefficients of the derivative at s=0 of a certain incoherent Eisenstein series for the group U(n, n). This is done by relating the arithmetic cycles to their formal counterpart from Part I via non-archimedean uniformization, and by relating the Fourier coefficients to the derivatives of representation densities of hermitian forms. The result then follows from the main theorem of Part I and a counting argument.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e9b26d91170035d4a31387aa0974a0adc7222ec7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Xuhua He
2. S. Nie
3. Chao Li
4. Wei Zhang
5. Ulrich Goertz
6. Wei Zhang
7. Michael Rapoport
8. C. Skinner

In Mathematical Physics

1. Xuhua He
2. S. Nie
3. Chao Li
4. Wei Zhang
5. Ulrich Goertz
6. Wei Zhang
7. Michael Rapoport
8. C. Skinner

Citations in the corpus

• Fully Hodge–Newton Decomposable Shimura Varieties (2016, background): “, [41, 42]) or in work toward Zhang’s Arithmetic Fundamental Lemma (e.”
• On arithmetic fundamental lemmas (2012, methodology): “5.2 Some preliminary results We now recall some results of Gross, Keating and Kudla–Rapoport (cf. [16]).”
• Kudla-Rapoport cycles and derivatives of local densities (2019, background): “3) generalizing the Kudla–Rapoport cycles Z(T ) in [KR14].”