• 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… 
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References

SHOWING 1-10 OF 68 REFERENCES
On the arithmetic moduli schemes of PEL Shimura varieties
Splitting metaplectic covers of dual reductive pairs
AbstractThe symplectic group Sp(N, F) over a local fieldF (other than ℂ) has a unique non-trivial twofold central extension. The inclusion of {±1} into the circle ℂ1 induces an extension $$1 \to C^1
Regular formal moduli spaces and arithmetic transfer conjectures
We define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic
Complex multiplication cycles and Kudla-Rapoport divisors, II
This paper is about the arithmetic of {\it Kudla-Rapoport divisors} on Shimura varieties of type ${\rm GU}(n-1,1)$. In the first part of the paper we construct a toroidal compactification of
8
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 of
Mathematische Annalen
Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für
Volume 73
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 and
Inventiones mathematicae
  • 84(2):321–326,
  • 1986
...
...