# On local representation densities of hermitian forms and special cycles

@inproceedings{Cho2021OnLR, title={On local representation densities of hermitian forms and special cycles}, author={Sungyoon Cho}, year={2021} }

. In this paper, we prove that there are certain relations among representation densities and provide an eﬃcient way to compute representation densities by using these relations. As an application, we compute some arithmetic intersection numbers of special cycles on unitary Shimura varieties and propose a conjecture on these.

## References

SHOWING 1-10 OF 11 REFERENCES

### Local Zeta Functions on Hermitian Forms and Its Application to Local Densities

- Mathematics
- 1998

Abstract We give an explicit description of functional equations satisfied by zeta functions on the space of unramified hermitian forms over a p -adic field. Further, as an application, we give…

### Arithmetic diagonal cycles on unitary Shimura varieties

- MathematicsCompositio Mathematica
- 2020

We define variants of PEL type of the Shimura varieties that appear in the context of the arithmetic Gan–Gross–Prasad (AGGP) conjecture. We formulate for them a version of the AGGP conjecture. We…

### Unitary cycles on Shimura curves and the Shimura lift II

- MathematicsCompositio Mathematica
- 2014

Abstract We consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles these…

### Kudla-Rapoport cycles and derivatives of local densities

- Mathematics
- 2019

We prove the local Kudla--Rapoport conjecture, which is a precise identity between the arithmetic intersection numbers of special cycles on unitary Rapoport--Zink spaces and the derivatives of local…

### IMPROPER INTERSECTIONS OF KUDLA–RAPOPORT DIVISORS AND EISENSTEIN SERIES

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2015

We consider a certain family of Kudla–Rapoport cycles on an integral model of a Shimura variety attached to a unitary group of signature (1, 1), and prove that the arithmetic degrees of these cycles…

### The basic locus of the unitary Shimura variety with parahoric level structure, and special cycles

- Mathematics
- 2019

In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\mathcal{M}^{ss}}$ is uniformized…

### Special cycles on unitary Shimura varieties I. Unramified local theory

- Mathematics
- 2008

The supersingular locus in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n−1) over ℚ is uniformized by a formal scheme $\mathcal{N}$. In the case when p is an inert…

### Chow groups and $L$-derivatives of automorphic motives for unitary groups

- MathematicsAnnals of Mathematics
- 2021

In this article, we study the Chow group of the motive associated to a tempered global $L$-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is…

### A reformulation of the Siegel series and intersection numbers

- MathematicsMathematische Annalen
- 2020

In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multiplicities of Gross and…