Corpus ID: 215768671

Special cycles on unitary Shimura curves at ramified primes

@article{Shi2020SpecialCO,
  title={Special cycles on unitary Shimura curves at ramified primes},
  author={Yousheng Shi},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
  • Yousheng Shi
  • Published 13 April 2020
  • Mathematics
  • arXiv: Algebraic Geometry
In this paper, we study special cycles on the Kramer model of $\mathrm{GU}(1,1)(F)$ Rapoport-Zink spaces where $F$ is a ramified extension of $\mathbb{Q}_p$ with the assumption that the underlying hermitian form on the Dieudonne module of the framing object of the Rapoport-Zink space is aniostropic. We write down the decomposition of these special cycles and compute their intersection numbers. We then apply the local results to compute the intersection numbers of special cycles on unitary… Expand
KUDLA-RAPOPORT CONJECTURE AT RAMIFIED PRIMES
  • YOUSHENG SHI, TONGHAI YANG
  • 2021
In this paper, we propose a modified Kudla-Rapoport conjecture for the Krämer model of unitary Rapoport-Zink space over a ramified prime, which is a precise identity relating intersection numbers ofExpand
Kudla program for unitary Shimura varieties
In this paper, we first review and summarize some recent progress in Kudla program on unitary Shimura varieties. We show how the local arithmetic Siegel-Weil formula implies the global arithmeticExpand
The Kudla-Rapoport conjecture at a ramified prime.
In this paper, we proved a local arithmetic Siegel-Weil formula for a $U(1, 1)$-Shimura variety at a ramified prime, a.k.a. a Kudla-Rapoport conjecture in a ramified case. The formula needs to beExpand

References

SHOWING 1-10 OF 61 REFERENCES
8.
  • When Bad Things Happen to Rich People
  • 2020
Special cycles on the basic locus of unitary Shimura varieties at ramified primes
  • arXiv preprint arXiv:1811.11227,
  • 2018
Special cycles on unitary Shimura varieties II: global theory
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 andExpand
Volume 73
Period Spaces for p-divisible Groups
In this monograph "p"-adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of "p"-adic period domains to moduli space ofExpand
Inventiones mathematicae
  • 84(2):321–326,
  • 1986
Mathematische Annalen
Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich fürExpand
Inventiones mathematicae
  • 184(3):629–682,
  • 2011
Algebraic Geometry and Arithmetic Curves
Introduction 1. Some topics in commutative algebra 2. General Properties of schemes 3. Morphisms and base change 4. Some local properties 5. Coherent sheaves and Cech cohmology 6. Sheaves ofExpand
Commentarii Mathematici Universitatis Sancti Pauli
  • 01
  • 2000
...
1
2
3
4
5
...